Quasiconformal maps in metric spaces with controlled geometry

DOI10.1007/BF02392747zbMath0915.30018WikidataQ112013116 ScholiaQ112013116MaRDI QIDQ1273529

Pekka Koskela, Juha Heinonen

Publication date: 23 March 1999

Published in: Acta Mathematica (Search for Journal in Brave)

zbMATH Keywords

quasiconformal mappingCarnot-Carathéodory space

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65)

Related Items (only showing first 100 items - show all)

\(d_p\)-convergence and \(\epsilon\)-regularity theorems for entropy and scalar curvature lower bounds ⋮ Coarea inequality for monotone functions on metric surfaces ⋮ Boundary behaviour of open, light mappings in metric measure spaces ⋮ Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry ⋮ Sobolev Spaces in Extended Metric-Measure Spaces ⋮ Brief Survey on Functions of Bounded Variation (BV) in Metric Setting ⋮ Quasiconformal mappings and curvatures on metric measure spaces ⋮ Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces ⋮ Existence and uniqueness of limits at infinity for homogeneous Sobolev functions ⋮ Harmonic functions and gravity localization ⋮ Neumann \(p\)-Laplacian problems with a reaction term on metric spaces ⋮ Quasisymmetric embeddings of slit Sierpiński carpets ⋮ A fibered Tukia theorem for nilpotent Lie groups ⋮ Weakly quasisymmetric mappings and uniform domains on generalized Grushin planes ⋮ Quasisymmetry and solidity of quasiconformal maps in metric spaces ⋮ Egg-yolk principle for uniformizing Gromov hyperbolic domains ⋮ Sobolev embeddings for fractional Hajłasz-Sobolev spaces in the setting of rearrangement invariant spaces ⋮ Fractional Poincaré and localized Hardy inequalities on metric spaces ⋮ Extensions and approximations of Banach-valued Sobolev functions ⋮ Volume growth, capacity estimates, \(p\)-parabolicity and sharp integrability properties of \(p\)-harmonic Green functions ⋮ Heat kernels, stochastic processes and functional inequalities. Abstracts from the workshop held October 30 -- November 5, 2022 ⋮ Non-Hilbertian tangents to Hilbertian spaces ⋮ Poincaré inequalities on graphs ⋮ Polyhedral approximation of metric surfaces and applications to uniformization ⋮ Stability of Sobolev inequalities on Riemannian manifolds with Ricci curvature lower bounds ⋮ Construction of 𝑝-energy and associated energy measures on Sierpiński carpets ⋮ Quasi‐invariance of modulus and quasisymmetry of weakly (L,M)‐quasisymmetric maps in metric spaces ⋮ Homeomorphisms between Finsler manifolds satisfying the Rohde condition ⋮ A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces ⋮ Capacitary density and removable sets for Newton-Sobolev functions in metric spaces ⋮ Quasisymmetry and quasihyperbolicity of mappings on John domains ⋮ Ricci curvature in dimension 2 ⋮ A note on indecomposable sets of finite perimeter ⋮ The general class of Wasserstein Sobolev spaces: density of cylinder functions, reflexivity, uniform convexity and Clarkson's inequalities ⋮ Removable sets for Newtonian Sobolev spaces and a characterization of \(p\)-path almost open sets ⋮ Non-locality, non-linearity, and existence of solutions to the Dirichlet problem for least gradient functions in metric measure spaces ⋮ On the radial limits of mappings on Riemannian manifolds ⋮ Metric space mappings connected with Sobolev-type function classes ⋮ Conformal Assouad dimension as the critical exponent for combinatorial modulus ⋮ Locally biHölder continuous maps and their induced embeddings between Besov spaces ⋮ Thin Loewner Carpets and Their Quasisymmetric Embeddings in S² ⋮ Sharp log-Sobolev inequalities in \(\mathsf{CD}(0, N)\) spaces with applications ⋮ Absolutely continuous mappings on doubling metric measure spaces ⋮ Trace and extension theorems for homogeneous Sobolev and Besov spaces for unbounded uniform domains in metric measure spaces ⋮ Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings ⋮ Absolute continuity in higher dimensions ⋮ Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential ⋮ Uniformity and Loewner condtions of metric spaces ⋮ Pullback of a quasiconformal map between arbitrary metric measure spaces ⋮ Topological mappings of finite area distortion ⋮ An axiomatic approach to gradients with applications to Dirichlet and obstacle problems beyond function spaces ⋮ Homeomorphisms of the Heisenberg group preserving BMO ⋮ Measure density and extension of Besov and Triebel-Lizorkin functions ⋮ Tangent lines and Lipschitz differentiability spaces ⋮ Higher integrability for vector-valued parabolic quasi-minimizers on metric measure spaces ⋮ The variational 1-capacity and BV functions with zero boundary values on doubling metric spaces ⋮ Necessity of a Wiener type condition for boundary regularity of quasiminimizers and nonlinear elliptic equations ⋮ A new approach to Sobolev spaces in metric measure spaces ⋮ Infinitesimal structure of differentiability spaces, and metric differentiation ⋮ Equivalence and self-improvement of \(p\)-fatness and Hardy's inequality, and association with uniform perfectness ⋮ Circle packings and combinatorial moduli ⋮ Quasisymmetric nonparametrization and spaces associated with the Whitehead continuum ⋮ On value distributions for quasimeromorphic mappings on \(\mathbb H\)-type Carnot groups ⋮ Gaussian heat kernel bounds through elliptic Moser iteration ⋮ Conformality and \(Q\)-harmonicity in Carnot groups ⋮ Characterizations of sets of finite perimeter using heat kernels in metric spaces ⋮ Absolute continuity of quasiconformal mapping of Carnot-Carathéodory spaces ⋮ Hölder regularity for parabolic De Giorgi classes in metric measure spaces ⋮ Extendability of classes of maps and new properties of upper sets ⋮ Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces ⋮ Regularity of sets with quasiminimal boundary surfaces in metric spaces ⋮ Wiener criterion on metric spaces: boundary regularity in axiomatic and Poincaré-Sobolev spaces ⋮ Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces ⋮ Newtonian Lorentz metric spaces ⋮ Mappings of finite distortion: reverse inequalities for the Jacobian ⋮ An upper gradient approach to weakly differentiable cochains ⋮ Prime ends for domains in metric spaces ⋮ Lusin-type theorems for Cheeger derivatives on metric measure spaces ⋮ Geometry and analysis of Dirichlet forms. II ⋮ BMO, integrability, Harnack and Caccioppoli inequalities for quasiminimizers ⋮ Pointwise characterizations of Besov and Triebel-Lizorkin spaces and quasiconformal mappings ⋮ The properties of quasisymmetric mappings in metric spaces ⋮ Characterizations of Orlicz-Sobolev spaces by means of generalized Orlicz-Poincaré inequalities ⋮ On quasisymmetry of quasiconformal mappings ⋮ Cluster sets for Sobolev functions and quasiminimizers ⋮ Local Poincaré inequalities from stable curvature conditions on metric spaces ⋮ On the geometry of a class of embeddings in the plane ⋮ Boundary behavior of mappings in \(\lambda(\epsilon)\)-regular metric spaces ⋮ \(p\)-Poincaré inequality versus \(\infty \)-Poincaré inequality: some counterexamples ⋮ Removable sets for Orlicz-Sobolev spaces ⋮ Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm ⋮ Flat forms, bi-Lipschitz parametrizations, and smoothability of manifolds ⋮ Gradient estimate for solutions to Poisson equations in metric measure spaces ⋮ Hajłasz gradients are upper gradients ⋮ The equivalence between pointwise Hardy inequalities and uniform fatness ⋮ Measurability of equivalence classes and MEC\(_p\)-property ⋮ Is an Orlicz-Poincaré inequality an open ended condition, and what does that mean? ⋮ Extensions and traces of functions of bounded variation on metric spaces ⋮ Minimal Ahlfors regular conformal dimension of coarse expanding conformal dynamics on the sphere ⋮ Gromov hyperbolic discrete spaces and their application to extension of classes of mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some remarks about metric spaces, spherical mappings, functions and their derivatives
• The boundary correspondence under quasiconformal mappings
• Extremal length and functional completion
• Uniformly elliptic operators on Riemannian manifolds
• Quasiconformal mappings onto John domains
• Quasiconformal mappings on the Heisenberg group
• Quasimöbius maps
• Quasiextremal distance domains and extension of quasiconformal mappings
• Quasiconformal maps of cylindrical domains
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Weighted Hardy spaces
• Sur les groupes hyperboliques d'après Mikhael Gromov. (On the hyperbolic groups à la M. Gromov)
• Conformal geometry and quasiregular mappings
• A p-extremal length and p-capacity equality
• A remark on quasiconformal mappings on Carnot groups
• The combinatorial Riemann mapping theorem
• Removable sets for Sobolev spaces
• Foundations for the theory of quasiconformal mappings on the Heisenberg group
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Definitions of quasiconformality
• The differential of a quasi-conformal mapping of a Carnot-Carathéodory space
• A capacity estimate on Carnot groups
• Sobolev spaces and harmonic maps for metric space targets
• Analysis on geodesic balls of sub-elliptic operators
• Isometric Riemannian manifolds at infinity
• Good metric spaces without good parameterizations
• Analytic properties of quasiconformal mappings on Carnot groups
• On the nonexistence of bilipschitz parameterizations and geometric problems about \(A_ \infty\)-weights
• Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities
• Extremal length and p-capacity
• Lectures on \(n\)-dimensional quasiconformal mappings
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• Dimension conforme et sphère à l'infini des variétés à courbure négative
• Symmetrization of Rings in Space
• An estimate for pseudoconformal capacities on the sphere
• Plongements lipschitziens dans ${\bbfR}\sp n$
• Quasi-Symmetric Embeddings in Euclidean Spaces
• A note on the isoperimetric constant
• Weighted norm inequalities for maximal functions and singular integrals
• Quasisymmetric embeddings of metric spaces
• Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
• Recognizing constant curvature discrete groups in dimension 3
• From local to global in quasiconformal structures.
• Un Groupe Hyperbolique Est Déterminé Par Son Bord
• Extension of Loewner's Capacity Theorem
• Strong Rigidity of Locally Symmetric Spaces. (AM-78)

This page was built for publication: Quasiconformal maps in metric spaces with controlled geometry