Modulus and Poincaré inequalities on non-self-similar Sierpiński carpets

DOI10.1007/s00039-013-0227-6zbMath1271.30032arXiv1201.3548OpenAlexW3102696762MaRDI QIDQ2376327

Jeremy T. Tyson, John M. Mackay, Kevin Wildrick

Publication date: 21 June 2013

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3548

zbMATH Keywords

Sierpinski carpetdoubling measurePoincare inequalityGromov-Hausdorff tangent cone

Mathematics Subject Classification ID

Fractals (28A80) Potential theory on fractals and metric spaces (31E05) Analysis on metric spaces (30L99)

Related Items (13)

Quasisymmetrically co-Hopfian Menger curves and Sierpiński spaces ⋮ INVISIBLE SETS AND CONFORMAL DIMENSIONS OF SQUARE SIERPIŃSKI CARPETS ⋮ Quasisymmetric embeddings of slit Sierpiński carpets ⋮ Conformal dimension via p-resistance: Sierpinski carpet ⋮ Topological Hausdorff dimension and Poincaré inequality ⋮ Thin Loewner Carpets and Their Quasisymmetric Embeddings in S² ⋮ Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential ⋮ Characterizing spaces satisfying Poincaré inequalities and applications to differentiability ⋮ Dimension distortion by Sobolev mappings in foliated metric spaces ⋮ Indecomposable sets of finite perimeter in doubling metric measure spaces ⋮ Sierpinski-type fractals are differentiably trivial ⋮ Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals ⋮ Isoperimetric and Poincaré inequalities on non-self-similar Sierpiński sponges: the borderline case

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