Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
From MaRDI portal
Publication:1124131
DOI10.2307/1971484zbMath0678.53042OpenAlexW2314781788WikidataQ56850582 ScholiaQ56850582MaRDI QIDQ1124131
Publication date: 1989
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/1971484
Discrete subgroups of Lie groups (22E40) Global Riemannian geometry, including pinching (53C20) Differential geometry of symmetric spaces (53C35)
Related Items
Bi-Lipschitz embeddings of quasiconformal trees ⋮ QUASI-ISOMETRY INVARIANTS AND ASYMPTOTIC CONES ⋮ Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings ⋮ On the smoothness of $C^1$-contact maps in $C^\infty$-rigid Carnot groups ⋮ A rectifiability result for finite-perimeter sets in Carnot groups ⋮ A Car as Parabolic Geometry ⋮ POINCARÉ AND SOBOLEV INEQUALITIES FOR DIFFERENTIAL FORMS IN HEISENBERG GROUPS AND CONTACT MANIFOLDS ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ A Rademacher type theorem for Hamiltonians \(H(x, p)\) and an application to absolute minimizers ⋮ Continuity of the mappings with finite distortion of the Sobolev class \(W^1_{\nu,\operatorname{loc}}\) on Carnot groups ⋮ Cauchy–Szegö commutators on weighted Morrey spaces ⋮ Generalised intermediate dimensions ⋮ A fibered Tukia theorem for nilpotent Lie groups ⋮ Unextendable Intrinsic Lipschitz Curves: ⋮ The Agrachev-Barilari-Boscain method and estimates for the number of segments of horizontal broken lines joining points in the canonical Carnot group \(G_{3,3}\) ⋮ Cone‐equivalent nilpotent groups with different Dehn functions ⋮ Unnamed Item ⋮ Carnot rectifiability of sub-Riemannian manifolds with constant tangent ⋮ Variational problems concerning sub-Finsler metrics in Carnot groups ⋮ Horizontal and straight triangulation on Heisenberg groups ⋮ Composing and decomposing surfaces and functions ⋮ Quasi‐invariance of modulus and quasisymmetry of weakly (L,M)‐quasisymmetric maps in metric spaces ⋮ \(q\)-Poincaré inequalities on Carnot groups with filiform type Lie algebra ⋮ A note on laminations with symmetric leaves ⋮ Conjugacy growth in the higher Heisenberg groups ⋮ Area formula for regular submanifolds of low codimension in Heisenberg groups ⋮ Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group ⋮ Two-step sub-Lorentzian structures and graph surfaces ⋮ Modulus of surface families and the radial stretch in the Heisenberg group ⋮ Rigidity of quasiconformal maps on Carnot groups ⋮ Quasi-isometries between groups with two-ended splittings ⋮ Openness and discreteness of mappings of finite distortion on Carnot groups ⋮ Classes of noncontact mappings of Carnot groups and metric properties ⋮ \( BV \)-spaces and the bounded composition operators of \(BV\)-functions on Carnot groups ⋮ Identifying 1-rectifiable measures in Carnot groups ⋮ Umbel convexity and the geometry of trees ⋮ Topological properties of mappings with finite distortion on Carnot groups ⋮ \(C^{1,\alpha}\)-rectifiability in low codimension in Heisenberg groups ⋮ Relative L^p-cohomology and application to Heintze groups ⋮ Horizontal joinability on 5-dimensional 2-step Carnot groups with a codimension 2 horizontal distribution ⋮ Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces ⋮ Intrinsic Lipschitz graphs in Carnot groups of step 2 ⋮ A $C^m$ Whitney extension theorem for horizontal curves in the Heisenberg group ⋮ Švarc–Milnor quasi-isometries for Fuchsian groups ⋮ The modulus of the Korányi ellipsoidal ring ⋮ LARGE-SCALE SUBLINEARLY LIPSCHITZ GEOMETRY OF HYPERBOLIC SPACES ⋮ MASS TRANSPORTATION IN GROUPS OF TYPE H ⋮ Maximal Surfaces on Two-Step Sub-Lorentzian Structures ⋮ Quasi-flats and rigidity in higher rank symmetric spaces ⋮ Thirty-three yes or no questions about mappings, measures, and metrics ⋮ On the Lipschitz dimension of Cheeger–Kleiner ⋮ Cohomological induction and uniform measure equivalence ⋮ Quasi-isometric rigidity of nonuniform lattices in higher rank symmetric spaces ⋮ Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds ⋮ Characterisation of the sub-Riemannian isometry groups of theH-type groups ⋮ Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces ⋮ Quasiisometries of negatively curved homogeneous manifolds associated with Heisenberg groups ⋮ Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group ⋮ Integral representations and embedding theorems for functions defined on the Heisenberg groups $\mathbb H^n$ ⋮ Asymptotic Cones and Ultrapowers of Lie Groups ⋮ Maximal convergence groups and rank one symmetric spaces ⋮ Rigidity of Teichmüller space ⋮ Lipschitz groups and Lipschitz maps ⋮ Global conformal Assouad dimension in the Heisenberg group ⋮ Contact equations, Lipschitz extensions and isoperimetric inequalities ⋮ Isomorphisms of Sobolev spaces on Carnot groups and quasiconformal mappings ⋮ The area formula for graphs on 4-dimensional 2-step sub-Lorentzian structures ⋮ The morphism property of subelliptic equations on the roto-translation group ⋮ On roughly transitive amenable graphs and harmonic Dirichlet functions ⋮ Geometry of Grushin spaces ⋮ Vanishing of cohomology and parameter rigidity of actions of solvable Lie groups, II ⋮ Intrinsic regular surfaces of low codimension in Heisenberg groups ⋮ Intrinsically Lipschitz functions with normal target in Carnot groups ⋮ Quasiconformal maps on a 2-step Carnot group ⋮ Induced quasi-actions: A remark ⋮ Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2 ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ Starshapedeness for fully non‐linear equations in Carnot groups ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ Translation-like actions of nilpotent groups ⋮ LIPSCHITZ CONTINUITY FOR H-CONVEX FUNCTIONS IN CARNOT GROUPS ⋮ Anti-de Sitter strictly GHC-regular groups which are not lattices ⋮ Contact and quasiconformal mappings on real model filiform groups ⋮ Almost additive entropy ⋮ Minimising Hausdorff dimension under Hölder equivalence ⋮ Unnamed Item ⋮ Geometric flow and rigidity on symmetric spaces of noncompact type ⋮ On groups with locally compact asymptotic cones ⋮ Unnamed Item ⋮ Limit sets of discrete groups of isometries of exotic hyperbolic spaces ⋮ Sets of minimal Hausdorff dimension for quasiconformal maps ⋮ Deformation of Schottky groups in complex hyperbolic space ⋮ Uniqueness of minimisers for a Grötzsch-Belinskiĭ type inequality in the Heisenberg group ⋮ Carnot metrics, dynamics and local rigidity ⋮ An explicit formula of Cauchy-Szego kernel for quaternionic Siegel upper half space and applications ⋮ Lipschitz graphs and currents in Heisenberg groups ⋮ Intrinsic regular hypersurfaces in Heisenberg groups ⋮ Horizontal joinability in canonical 3-step Carnot groups with corank 2 horizontal distributions ⋮ Exact values of constants in the generalized triangle inequality for some \((1, q_2)\)-quasimetrics on canonical Carnot groups ⋮ A loop group method for affine harmonic maps into Lie groups ⋮ Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs ⋮ Visibility metrics on the infinity boundary of the complex hyperbolic plane ⋮ Some examples of quasiisometries of nilpotent Lie groups ⋮ 1-quasiconformal mappings on a (2,2)-type quadric ⋮ Coarse differentiation and multi-flows in planar graphs ⋮ On the cross-ratio at the boundary of \(CAT(-1)\)-spaces ⋮ Monotone functions and quasiconformal mappings on Carnot groups ⋮ Normal families of mappings on Carnot groups ⋮ Approximately differentiable transformations and change of variables on nilpotent groups ⋮ Aperiodic tilings ⋮ On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups ⋮ Conformality and \(Q\)-harmonicity in Carnot groups ⋮ Lusin approximation for horizontal curves in step 2 Carnot groups ⋮ The tangent space in sub-Riemannian geometry ⋮ A joinings classification and a special case of Raghunathan's conjecture in positive characteristic (with an appendix by Kevin Wortman) ⋮ Absolute continuity of quasiconformal mapping of Carnot-Carathéodory spaces ⋮ The Teichmüller distance on the space of spherical CR structures ⋮ Markov type and threshold embeddings ⋮ Quasi-isometric rigidity and Diophantine approximation ⋮ Generalized Hadamard's inequality and \(r\)-convex functions in Carnot groups ⋮ Regular submanifolds, graphs and area formula in Heisenberg groups ⋮ Lipschitz and path isometric embeddings of metric spaces ⋮ The tangent cone to a quasimetric space with dilations ⋮ On one class of Lipschitz vector fields in \(\mathbb R^{3}\) ⋮ Metric differentiation, monotonicity and maps to \(L^{1}\) ⋮ Sub-Riemannian geometry of the coefficients of univalent functions ⋮ Quasiregular maps on Carnot groups ⋮ Hypersurfaces and variational formulas in sub-Riemannian Carnot groups ⋮ Differentiability of mappings of Carnot manifolds and isomorphism of tangent cones ⋮ Dirichlet problem at infinity for harmonic maps between Carnot spaces ⋮ Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings ⋮ Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation ⋮ Compression bounds for Lipschitz maps from the Heisenberg group to \(L_{1}\) ⋮ A characterization of sub-Riemannian spaces as length dilation structures constructed via coherent projections ⋮ Harmonic morphisms from homogeneous Hadamard manifolds ⋮ Geometry and rigidity of mapping class groups. ⋮ Two-scale homogenization in the Heisenberg group ⋮ Extremal length for quasiregular mappings on Heisenberg groups. ⋮ On the structure of finite perimeter sets in step 2 Carnot groups ⋮ Boundary behavior of mappings in \(\lambda(\epsilon)\)-regular metric spaces ⋮ Isomorphisms of Sobolev spaces on Carnot groups and metric properties of mappings ⋮ Quasisymmetric maps on the boundary of a negatively curved solvable Lie group ⋮ Pattern rigidity and the Hilbert-Smith conjecture. ⋮ Coarse differentiation of quasi-isometries. I: Spaces not quasi-isometric to Cayley graphs ⋮ Differentiability of intrinsic Lipschitz functions within Heisenberg groups ⋮ Discrete actions on nilpotent Lie groups and negatively curved spaces. ⋮ Composition operators in weighted Sobolev spaces on Carnot groups ⋮ Optimal mass transportation in the Heisenberg group. ⋮ Hausdorff dimensions of limit sets. I ⋮ Vertical versus horizontal Poincaré inequalities on the Heisenberg group ⋮ Differential forms in Carnot groups: a \(\Gamma \)-convergence approach ⋮ Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem ⋮ Geodesic manifolds with a transitive subset of smooth biLipschitz maps ⋮ Isomorphisms of Sobolev spaces on Carnot groups and quasi-isometric mappings ⋮ Regularity of sets with constant intrinsic normal in a class of Carnot groups ⋮ Ultrarigid tangents of sub-Riemannian nilpotent groups ⋮ Privileged coordinates and nilpotent approximation of Carnot manifolds. I: General results ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ BiLipschitz decomposition of Lipschitz maps between Carnot groups ⋮ Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\) ⋮ On the quantitative quasi-isometry problem: transport of Poincaré inequalities and different types of quasi-isometric distortion growth ⋮ Foliated Plateau problem. II: Harmonic maps of foliations ⋮ Foliated Plateau problem. I: Minimal varieties ⋮ Markov convexity and nonembeddability of the Heisenberg group ⋮ Lipschitz extensions of maps between Heisenberg groups ⋮ Weak capacity and modulus comparability in Ahlfors regular metric spaces ⋮ Quaternionic contact hypersurfaces in hyper-Kähler manifolds ⋮ Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds ⋮ On derivations of subalgebras of real semisimple Lie algebras ⋮ Modules of systems of measures on polarizable Carnot groups ⋮ Differentiability of integrable measurable cocycles between nilpotent groups ⋮ Polynomial sub-Riemannian differentiability on Carnot groups ⋮ Quasiconformal deformations of complex hyperbolic \(p\)-Schottky groups ⋮ Maximal graph surfaces on four-dimensional two-step sub-Lorentzian structures ⋮ Conformal quaternionic contact curvature and the local sphere theorem ⋮ Bourgain's discretization theorem ⋮ Inverse and implicit function theorems on Carnot manifolds ⋮ Differentiating maps into \(L^1\), and the geometry of BV functions ⋮ Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips ⋮ Counter example to the Besicovitch covering property for some Carnot groups equipped with their Carnot-Carathéodory metric ⋮ Spaces and groups with conformal dimension greater than one ⋮ Conformal mappings and CR mappings on the Engel group ⋮ Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem ⋮ Hardy-Littlewood inequality for quasiregular maps on Carnot groups ⋮ Aronsson's equations on Carnot-Carathéodory spaces ⋮ Tangent cone to a regular quasimetric Carnot-Carathéodory space ⋮ Vanishing of the first reduced cohomology with values in an \(L^p\)-representation ⋮ The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups ⋮ Quasiconformal maps in metric spaces with controlled geometry ⋮ Boundary behavior of nonnegative solutions of subelliptic equations in NTA domains for Carnot-Carathéodory metrics ⋮ Sobolev spaces and \((P,Q)\)-quasiconformal mappings of Carnot groups ⋮ Mostow strong rigidity of locally symmetric spaces revisited ⋮ Rigidity of integral curves of rank 2 distributions ⋮ Sharp differentiability results for the lower local Lipschitz constant and applications to non-embedding ⋮ Isometries of Carnot groups and sub-Finsler homogeneous manifolds ⋮ Lipschitz continuity, Aleksandrov theorem and characterizations for \(H\)-convex functions ⋮ Hölder mappings of Carnot groups and intrinsic bases ⋮ The polynomial sub-Riemannian differentiability of some Hölder mappings of Carnot groups ⋮ Nonnegative kernels and 1-rectifiability in the Heisenberg group ⋮ Boundary at infinity of symmetric rank one spaces ⋮ Nonsmooth calculus ⋮ Geodesic inversion and Sobolev spaces on Heisenberg type groups ⋮ A GENERALIZATION OF HAUSDORFF DIMENSION APPLIED TO HILBERT CUBES AND WASSERSTEIN SPACES ⋮ WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS ⋮ Metric Characterizations of Some Classes of Banach Spaces ⋮ Global contact and quasiconformal mappings of Carnot groups ⋮ Quasiregular mappings on sub-Riemannian manifolds ⋮ Intrinsic Lipschitz graphs within Carnot groups ⋮ Sharp geometric rigidity of isometries on Heisenberg groups ⋮ Sub-Riemannian calculus on hypersurfaces in Carnot groups ⋮ Quasi-convex functions in Carnot groups ⋮ The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations ⋮ On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target ⋮ Cheeger-différentiabilité d'applications de certains espaces de Sobolev ⋮ A measure zero universal differentiability set in the Heisenberg group ⋮ Orlicz spaces and the large scale geometry of Heintze groups ⋮ Differentiation of the convolution on the roto-translation group ⋮ Liouville theorem, conformally invariant cones and umbilical surfaces for Grushin-type metrics ⋮ Rigid two-step nilpotent Lie groups relative to multicontact structures ⋮ Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint. ⋮ A variant of Gromov's problem on Hölder equivalence of Carnot groups ⋮ Pliability, or the Whitney extension theorem for curves in Carnot groups ⋮ Infinite-dimensional Carnot groups and Gâteaux differentiability ⋮ Asymptotic behaviours in fractional Orlicz-Sobolev spaces on Carnot groups ⋮ Sub-Finsler structures from the time-optimal control viewpoint for some nilpotent distributions ⋮ Surface area on two-step sub-Lorentzian structures with multi-dimensional time ⋮ The coarea formula for vector functions on Carnot groups with sub-Lorentzian structure ⋮ Multiexponential maps in Carnot groups with applications to convexity and differentiability ⋮ On quasi-isometry invariants associated to a Heintze group ⋮ Porosity, differentiability and Pansu's theorem ⋮ Sub-Lorentzian coarea formula for mappings of Carnot groups ⋮ Quantitative measure equivalence between amenable groups ⋮ Hardy spaces and quasiconformal maps in the Heisenberg group ⋮ Sub-Finsler problem on the Cartan group ⋮ The almost Schur lemma in quaternionic contact geometry ⋮ Geometric invariance of the semi-classical calculus on nilpotent graded Lie groups ⋮ Measure of images of contact mappings on two-step sub-Lorentzian structures ⋮ Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces ⋮ Quaternionic Kähler and \(\mathrm{Spin}(7)\) metrics arising from quaternionic contact Einstein structures ⋮ On perturbations of two general equations in several variables ⋮ A \(C^{m,\omega}\) Whitney extension theorem for horizontal curves in the Heisenberg group ⋮ Hyperbolic groups with low-dimensional boundary ⋮ A weakly second-order differential structure on rectifiable metric measure spaces ⋮ Large scale geometry of negatively curved \(\mathbb{R}^n\rtimes\mathbb{R}\) ⋮ CONTACT AND PANSU DIFFERENTIABLE MAPS ON CARNOT GROUPS ⋮ Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group ⋮ Lipschitz homotopy groups of the Heisenberg groups ⋮ Monge's transport problem in the Heisenberg group ⋮ Conformal Graph Directed Markov Systems on Carnot Groups ⋮ Quasi-isometry and Rigidity ⋮ Optimal Bang-Bang Trajectories in Sub-Finsler Problems on the Engel Group ⋮ A global inverse map theorem and biLipschitz maps in the Heisenberg group ⋮ Metric normal and distance function in the Heisenberg group ⋮ Unnamed Item ⋮ Relatively Free Nilpotent Torsion-Free Groups and Their Lie Algebras ⋮ Differentiability of curves in the category of Carnot manifolds ⋮ Metric and geometric quasiconformality in Ahlfors regular Loewner spaces ⋮ A Bowen type rigidity theorem for non-cocompact hyperbolic groups ⋮ Tangent Halfspaces to Sets of Finite Perimeter in Carnot Groups ⋮ Contact and conformal maps in parabolic geometry ⋮ Quasiflats with holes in reductive groups. ⋮ Commensurability of hyperbolic manifolds with geodesic boundary ⋮ Blow-up of regular submanifolds in Heisenberg groups and applications ⋮ Generalized differentiation and bi-Lipschitz nonembedding in \(L^{1}\) ⋮ Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group \(\mathbb H^n\) ⋮ Sobolev Mappings between Manifolds and Metric Spaces ⋮ Sobolev spaces and the Cayley transform ⋮ New properties of convex functions in the Heisenberg group ⋮ On some nonuniform cases of the weighted Sobolev and Poincaré inequalities ⋮ Logarithmic potentials and quasiconformal flows on the Heisenberg group ⋮ Boolean percolation on doubling graphs ⋮ Lattice envelopes ⋮ APPROXIMATIONS OF SOBOLEV NORMS IN CARNOT GROUPS ⋮ Sub-Finsler structures on the Engel group ⋮ Analogues of Korn's inequality on Heisenberg groups ⋮ Level sets of classes of mappings of two-step Carnot groups in a nonholonomic interpretation ⋮ The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group ⋮ A sub-Finsler problem on the Cartan group ⋮ Cone unrectifiable sets and non-differentiability of Lipschitz functions ⋮ Isomorphisms between spaces of Lipschitz functions ⋮ Unnamed Item ⋮ Gradings on Lie algebras, systolic growth, and cohopfian properties of nilpotent groups ⋮ Discrete uniformizing metrics on distributional limits of sphere packings ⋮ TSALLIS ENTROPY COMPOSITION AND THE HEISENBERG GROUP ⋮ A continuation method for motion-planning problems ⋮ A note on the engulfing property and the $\Gamma ^{1+ \alpha }$-regularity of convex functions in Carnot groups ⋮ Length spectrum in rank one symmetric space is not arithmetic ⋮ Quasiconformally instable disc bundles with complex structures ⋮ Contact quasiconformal immersions ⋮ Quasi-conformal maps on model filiform groups ⋮ TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS ⋮ Geodesics and horizontal-path spaces in Carnot groups ⋮ BV functions and sets of finite perimeter in sub-Riemannian manifolds ⋮ Asymptotic invariants, complexity of groups and related problems ⋮ Metric spaces nonembeddable into Banach spaces with the Radon–Nikodým property and thick families of geodesics ⋮ Hierarchically hyperbolic spaces. I: Curve complexes for cubical groups ⋮ Left-invariant distributions diffeomorphic to flat distributions ⋮ Uniformity of \(cc\)-balls on some class of 2-step Carnot groups ⋮ Functional and analytical properties of a class of mappings of quasiconformal analysis on Carnot groups ⋮ Singular subelliptic equations and Sobolev inequalities on Carnot groups ⋮ On rectifiable measures in Carnot groups: Marstrand-Mattila rectifiability criterion ⋮ Approximate lattices ⋮ Metric equivalences of Heintze groups and applications to classifications in low dimension ⋮ Area of intrinsic graphs and coarea formula in Carnot groups ⋮ Universal differentiability sets and maximal directional derivatives in Carnot groups ⋮ Rigidity for convex-cocompact actions on rank-one symmetric spaces ⋮ Quasi-isometric embeddings of symmetric spaces ⋮ Nash \(C^ 1\)-embedding theorem for Carnot-Carathéodory metrics ⋮ The length and area principle for a function on an abstract surface over a domain of a Carnot group ⋮ Uniform domains and quasiconformal mappings on the Heisenberg group ⋮ Vertical perimeter versus horizontal perimeter ⋮ A reverse coarea-type inequality in Carnot groups ⋮ The differential of a quasi-conformal mapping of a Carnot-Carathéodory space ⋮ Rigidity of 2-step Carnot groups ⋮ On quotients of spaces with Ricci curvature bounded below ⋮ A framework for differential calculus on persistence barcodes ⋮ On the logarithmic coarse structures of Lie groups and hyperbolic spaces ⋮ Singular integrals on \(C^{1, \alpha}\) regular curves in Carnot groups ⋮ Isometric embeddings into Heisenberg groups ⋮ The quasi-isometry classification of rank one lattices ⋮ On exterior differential systems involving differentials of Hölder functions ⋮ Analytic properties of quasiconformal mappings on Carnot groups ⋮ Maximal surfaces on five-dimensional group structures ⋮ Porosity and differentiability of Lipschitz maps from stratified groups to Banach homogeneous groups ⋮ Non-embedding theorems of nilpotent Lie groups and sub-Riemannian manifolds ⋮ On local metric characteristics of level sets of \(C_H^1\)-mappings of Carnot manifolds ⋮ \(\Gamma \)-convergence of variational functionals with boundary terms in Stein manifolds ⋮ A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries ⋮ An introduction to the Ribe program ⋮ Estimates on the Markov convexity of Carnot groups and quantitative nonembeddability ⋮ Area formulas for classes of Hölder continuous mappings of Carnot groups ⋮ Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces ⋮ Classes of maximal surfaces on Carnot groups ⋮ Sobolev mappings and moduli inequalities on Carnot groups ⋮ The area of graphs on arbitrary Carnot groups with sub-Lorentzian structure ⋮ Groups quasi-isometric to right-angled Artin groups ⋮ Bi-Lipschitz extension from boundaries of certain hyperbolic spaces ⋮ On Ulam stability of a functional equation ⋮ Mappings with bounded \((P,Q)\)-distortion on Carnot groups ⋮ On the quasisymmetric Hölder-equivalence problem for Carnot groups ⋮ Automorphism groups of pseudo \(H\)-type algebras ⋮ A metric characteristic of minimal surfaces on arbitrary Carnot groups ⋮ Universal differentiability sets in Carnot groups of arbitrarily high step ⋮ The regularity of inverses to Sobolev mappings and the theory of \(\mathcal{Q}_{q,p} \)-homeomorphisms ⋮ Intrinsic differentiability and intrinsic regular surfaces in Carnot groups ⋮ Tubular neighborhoods in the sub-Riemannian Heisenberg groups ⋮ Almost bi-Lipschitz embeddings using covers of balls centred at the origin ⋮ A classification of sub-Riemannian manifolds ⋮ A survey of singular curves in sub-Riemannian geometry ⋮ Tangent maps and tangent groupoid for Carnot manifolds ⋮ Mappings with bounded distortion and with finite distortion on Carnot groups ⋮ Polynomial sub-Riemannian differentiability on Carnot-Carathéodory spaces ⋮ Sub-Finsler geodesics on the Cartan group ⋮ Harmonic quasi-isometric maps into Gromov hyperbolic \(\operatorname{CAT}(0)\)-spaces ⋮ The Whitney extension theorem for \(C^1\), horizontal curves in the Heisenberg group ⋮ Quantitative bi-Lipschitz embeddings of bounded-curvature manifolds and orbifolds ⋮ Structure of porous sets in Carnot groups ⋮ Coarea formula for functions on 2-step Carnot groups with sub-Lorentzian structure ⋮ Space-likeness of classes of level surfaces on Carnot groups and their metric properties ⋮ A \(C^m\) Lusin approximation theorem for horizontal curves in the Heisenberg group ⋮ Quasi-isometric embeddings of symmetric spaces and lattices: reducible case ⋮ Notion of \(\mathbb{H}\)-orientability for surfaces in the Heisenberg group \(\mathbb{H}^n\) ⋮ Conformality and \(Q\)-harmonicity in sub-Riemannian manifolds ⋮ Embedding the Heisenberg group into a bounded-dimensional Euclidean space with optimal distortion ⋮ Coarse differentiation and quantitative nonembeddability for Carnot groups ⋮ The Beltrami equations for quasiconformal mappings on strongly pseudoconvex hypersurfaces ⋮ The graphs of Lipschitz functions and minimal surfaces on Carnot groups ⋮ Graphs of Lipschitz functions and minimal surfaces on Carnot groups ⋮ Heat flow and quantitative differentiation ⋮ Isometries of nilpotent metric groups ⋮ Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane ⋮ Capacity of a condenser in the Heisenberg group ⋮ Complete classification of pseudo \(H\)-type algebras. II ⋮ Harmonic analysis, cohomology, and the large-scale geometry of amenable groups ⋮ Inequalities of Hadamard type for \(r\)-convex functions in Carnot groups ⋮ Sub-Riemannian currents and slicing of currents in the Heisenberg group \(\mathbb{H}^n\) ⋮ The qc Yamabe problem on non-spherical quaternionic contact manifolds ⋮ Minimal graph-surfaces on arbitrary two-step Carnot groups ⋮ Toward a quasi-Möbius characterization of invertible homogeneous metric spaces ⋮ Analogs of Korn's inequality on Heisenberg groups ⋮ Sub-Finsler horofunction boundaries of the Heisenberg group ⋮ Harmonic quasi-isometric maps. II: Negatively curved manifolds ⋮ A koebe distortion theorem for quasiconformal mappings in the Heisenberg group ⋮ The Yamabe operator and invariants on octonionic contact manifolds and convex cocompact subgroups of \(F_{4(-20)}\) ⋮ A differentiable structure for metric measure spaces ⋮ Conformal growth rates and spectral geometry on distributional limits of graphs ⋮ Rigidity, counting and equidistribution of quaternionic Cartan chains ⋮ Optimal horizontal joinability on the Engel group ⋮ Polynomial and horizontally polynomial functions on Lie groups ⋮ Some remarks on the definition of tangent cones in a Carnot-Carathéodory space ⋮ Lipschitz algebras and derivations. II: Exterior differentiation ⋮ At the boundary of some hyperbolic polyhedra ⋮ Definitions of quasiconformality ⋮ A cornucopia of Carnot groups in low dimensions ⋮ On the asymptotic geometry of Abelian-by-cyclic groups ⋮ Sobolev classes of Banach space-valued functions and quasiconformal mappings ⋮ On the approximability and parametrization of preimages of elements of Carnot groups on sub-Lorentzian structures
