Metric and geometric quasiconformality in Ahlfors regular Loewner spaces

DOI10.1090/S1088-4173-01-00064-9zbMath0981.30015OpenAlexW1643316420MaRDI QIDQ2761199

Jeremy T. Tyson

Publication date: 17 December 2001

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1088-4173-01-00064-9

zbMATH Keywords

Poincaré inequalityconformal modulusHausdorff/packing measureLoewner conditionquasiconformal/quasisymmetric map

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Harmonic analysis on homogeneous spaces (43A85) Hausdorff and packing measures (28A78)

Related Items (30)

Nonsmooth calculus ⋮ Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings ⋮ Polynomial control on stability, inversion and powers of matrices on simple graphs ⋮ Large scale geometry of certain solvable groups. ⋮ Circle packings and combinatorial moduli ⋮ Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary. ⋮ Orlicz spaces and the large scale geometry of Heintze groups ⋮ Quasiconformality to quasisymmetry via weak (L,M)-quasisymmetry ⋮ Stability for localized integral operators on weighted spaces of homogeneous type ⋮ Weakly quasisymmetric mappings and uniform domains on generalized Grushin planes ⋮ Norm-controlled inversion in Banach algebras of integral operators ⋮ The properties of quasisymmetric mappings in metric spaces ⋮ Quasi‐invariance of modulus and quasisymmetry of weakly (L,M)‐quasisymmetric maps in metric spaces ⋮ Sampling and reconstruction of signals in a reproducing kernel space with mixed norm ⋮ Boundary behavior of mappings in \(\lambda(\epsilon)\)-regular metric spaces ⋮ Quasisymmetric maps on the boundary of a negatively curved solvable Lie group ⋮ Large scale geometry of negatively curved \(\mathbb{R}^n\rtimes\mathbb{R}\) ⋮ Stability of Localized Integral Operators on Normal Spaces of Homogeneous Type ⋮ Rate of innovation for (non-)periodic signals and optimal lower stability bound for filtering ⋮ The quasiconformal subinvariance property of John domains in \({\mathbb {R}}^n\) and its applications ⋮ Duality of moduli in regular metric spaces ⋮ Average sampling and reconstruction in a reproducing kernel subspace of homogeneous type space ⋮ Local properties of quasihyperbolic mappings in metric spaces ⋮ Random sampling and reconstruction of concentrated signals in a reproducing kernel space ⋮ A koebe distortion theorem for quasiconformal mappings in the Heisenberg group ⋮ Sphericalization and flattening ⋮ Sobolev functions in the critical case are uniformly continuous in $s$-Ahlfors regular metric spaces when $s\le 1$ ⋮ Discrete uniformizing metrics on distributional limits of sphere packings ⋮ Quasi-conformal maps on model filiform groups ⋮ Quasihyperbolic metric and Quasisymmetric mappings in metric spaces

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