Quasiconformal mappings on the Heisenberg group

DOI10.1007/BF01388609zbMath0567.30017OpenAlexW2012722396MaRDI QIDQ1059736

Publication date: 1985

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143233

zbMATH Keywords

Heisenberg group contact structure

Mathematics Subject Classification ID

General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Analysis on other specific Lie groups (43A80) Quasiconformal mappings in the complex plane (30C62)

Related Items

Boundary behaviour of open, light mappings in metric measure spaces, Cauchy–Szegö commutators on weighted Morrey spaces, Weakly quasisymmetric mappings and uniform domains on generalized Grushin planes, On the radial limits of mappings on Riemannian manifolds, Left-invariant distributions diffeomorphic to flat distributions, Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group, The polynomial sub-Riemannian differentiability of some Hölder mappings of Carnot groups, Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings, Geodesic inversion and Sobolev spaces on Heisenberg type groups, WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS, Compensated compactness and the Heisenberg group, Global contact and quasiconformal mappings of Carnot groups, Erratum: ``Compensated compactness and the Heisenberg group, Quasiregular mappings on sub-Riemannian manifolds, The Heisenberg group associated to a Hilbert space, Rigidity for convex-cocompact actions on rank-one symmetric spaces, Some examples of quasiisometries of nilpotent Lie groups, 1-quasiconformal mappings on a (2,2)-type quadric, Quasiconformal homeomorphisms on CR 3-manifolds with symmetries, Eigenforms of the Laplacian on real and complex hyperbolic spaces, A characterization of constant $p$-mean curvature surfaces in the Heisenberg group $H_1$, Conformality and $Q$-harmonicity in Carnot groups, $L^{p}$ and BMO bounds for weighted Hardy operators on the Heisenberg group, An approach to studying quasiconformal mappings on generalized Grushin planes, Liouville theorem, conformally invariant cones and umbilical surfaces for Grushin-type metrics, Rigid two-step nilpotent Lie groups relative to multicontact structures, Quasiconformal mappings of the motion group of the plane, Feeling the heat in a group of Heisenberg type, Spherical CR-manifolds of dimension 3, The local behaviour of open, light mappings satisfying generalized modular inequalities, Hardy space estimates of Hausdorff operators on the Heisenberg group, A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces, Quasiregular maps on Carnot groups, On local metric characteristics of level sets of $C_H^1$-mappings of Carnot manifolds, A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries, Area formulas for classes of Hölder continuous mappings of Carnot groups, Faraday's form and Maxwell's equations in the Heisenberg group, Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere, Modulus of surface families and the radial stretch in the Heisenberg group, Algebraic prolongation and rigidity of Carnot groups, Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group, An inner product formula on two-dimensional complex hyperbolic space, Conformal and CR mappings on Carnot groups, The modulus of the Korányi ellipsoidal ring, Symmetry algebra for multi-contact structures given by $2n$ vector fields on $\mathbb R^{2n+1}$, Optimal mass transportation in the Heisenberg group., DISCRETE AND DENSE SUBGROUPS ACTING ON COMPLEX HYPERBOLIC SPACE, Resolvent of the Laplacian on strictly pseudoconvex domains, Conformal Graph Directed Markov Systems on Carnot Groups, The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds, Bi-Lipschitz maps in $Q$-regular Loewner spaces, Area-stationary surfaces in the Heisenberg group $\mathbb H^1$, Moduli of Legendrian foliations and quadratic differentials in the Heisenberg group, A global inverse map theorem and biLipschitz maps in the Heisenberg group, Rigidity of Carnot groups relative to multicontact structures, Thirty-three yes or no questions about mappings, measures, and metrics, Sub-Riemannian Geometry and Hypoelliptic Operators, Ricci nilsoliton black holes, Quasiregular mappings of the Heisenberg group, Modules of systems of measures on polarizable Carnot groups, Tanaka prolongation of free Lie algebras, Conformality and $Q$-harmonicity in sub-Riemannian manifolds, Quasiconformal deformations of complex hyperbolic $p$-Schottky groups, Uniformly quasiregular maps on the compactified Heisenberg group, Metric and geometric quasiconformality in Ahlfors regular Loewner spaces, Characterisation of the sub-Riemannian isometry groups of theH-type groups, Degenerating the complex hyperbolic ideal triangle groups, Contact and conformal maps in parabolic geometry, Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips, Conformal mappings and CR mappings on the Engel group, The geometry of the Eisenstein-Picard modular group, Asymptotic upper curvature bounds in coarse geometry, Metric properties of level surfaces of Hölder mappings defined on two-step Carnot groups, Geometric construction of quasiconformal mappings in the Heisenberg group, Analogs of Korn's inequality on Heisenberg groups, On the class of Hölder surfaces in Carnot-Carathéodory spaces, Global conformal Assouad dimension in the Heisenberg group, On Three-Dimensional Cauchy-Riemann Manifolds, Boundedness of Hausdorff operators on Hardy spaces in the Heisenberg group, Diffusion by optimal transport in Heisenberg groups, Sobolev spaces and the Cayley transform, Modulus of revolution rings in the heisenberg group, Logarithmic potentials and quasiconformal flows on the Heisenberg group, Sharp estimates for geometric rigidity of isometries on the first Heisenberg group, The weighted $L^p$ and $\text{BMO}$ estimates for fractional Hausdorff operators on the Heisenberg group, $H$-type groups and Iwasawa decompositions, On the transverse beltrami equation, Weighted Morrey estimates for Hausdorff operator and its commutator on the Heisenberg group, The geometry of complex hyperbolic packs, Contact and quasiconformal mappings on real model filiform groups, Quasiconformal maps in metric spaces with controlled geometry, Level sets of classes of mappings of two-step Carnot groups in a nonholonomic interpretation, Prescribing the behaviour of geodesics in negative curvature, On boundary behaviour of symplectomorphisms, Unnamed Item, Mostow strong rigidity of locally symmetric spaces revisited, A cornucopia of Carnot groups in low dimensions, On mappings with bounded distortion on Heisenberg group, Cluster sets theorems on metric measure spaces, Transverse curves and chain curvature in the Heisenberg group., Deformation of Schottky groups in complex hyperbolic space, Uniqueness of minimisers for a Grötzsch-Belinskiĭ type inequality in the Heisenberg group, Sobolev classes of Banach space-valued functions and quasiconformal mappings, An explicit formula of Cauchy-Szego kernel for quaternionic Siegel upper half space and applications, Sharp estimates for Hardy operators on Heisenberg group, Lipschitz graphs and currents in Heisenberg groups

Cites Work