Thin Loewner Carpets and Their Quasisymmetric Embeddings in S2

DOI10.1002/cpa.22029arXiv1910.02394OpenAlexW3214987290MaRDI QIDQ6179345

Sylvester Eriksson-Bique, Jeff Cheeger

Publication date: 16 December 2023

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.02394

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Fractals (28A80) Quasiconformal mappings in metric spaces (30L10) Embeddings of discrete metric spaces into Banach spaces; applications in topology and computer science (46B85) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

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
• Combinatorial modulus on boundary of right-angled hyperbolic buildings
• Infinitesimal structure of differentiability spaces, and metric differentiation
• Quasisymmetric Koebe uniformization
• The Poincaré inequality does not improve with blow-up
• Strong \(A_\infty\)-weights are \(A_\infty\)-weights on metric spaces
• Nonlinear potential theory on metric spaces
• Uniformization of Sierpiński carpets in the plane
• Circle packings and combinatorial moduli
• Quasiconformal dimensions of selfsimilar fractals
• Poincaré inequalities, uniform domains and extension properties for Newton-Sobolev functions in metric spaces
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• On the structure of spaces with Ricci curvature bounded below. I
• Quasisymmetric parametrizations of two-dimensional metric spheres
• Modulus and the Poincaré inequality on metric measure spaces
• Lectures on analysis on metric spaces
• Rigidity of quasi-isometries for some hyperbolic buildings
• Sobolev classes of Banach space-valued functions and quasiconformal mappings
• Characterizing spaces satisfying Poincaré inequalities and applications to differentiability
• Conformal Assouad dimension and modulus
• Local and semilocal Poincaré inequalities on metric spaces
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Modelling porous structures by repeated Sierpinski carpets
• The Stepanov differentiability theorem in metric measure spaces
• Finding curves on general spaces through quantitative topology, with applications to Sobolev and Poincaré inequalities
• Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups.
• Quasisymmetric rigidity of square Sierpiński carpets
• Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
• Lower bounds for codimension-1 measure in metric manifolds
• Potential theory on Sierpiński carpets. With applications to uniformization
• Inverse limit spaces satisfying a Poincaré inequality
• Poincaré inequalities for mutually singular measures
• Modulus and Poincaré inequalities on non-self-similar Sierpiński carpets
• Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary.
• Geometric implications of the Poincaré inequality
• Hyperbolic groups with planar boundaries
• Über eine Eigenschaft der ebenen Komplexe
• Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon-Nikodym property
• Hyperbolic groups with low-dimensional boundary
• Martingales in Banach Spaces
• Dimension conforme et sphère à l'infini des variétés à courbure négative
• Topological characterization of the Sierpiński curve
• Rigidity of Schottky sets
• Quasisymmetric embeddings of metric spaces
• Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
• Cohomologie ℓp espaces de Besov
• PLANE WITH $A_{\infty}$ -WEIGHTED METRIC NOT BILIPSCHITZ EMBEDDABLE TO ${\bb R}^n$
• Differentiability, porosity and doubling in metric measure spaces
• Quasisymmetric embeddability of weak tangents
• PI spaces with analytic dimension 1 and arbitrary topological dimension
• Structure of measures in Lipschitz differentiability spaces
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

This page was built for publication: Thin Loewner Carpets and Their Quasisymmetric Embeddings in S²