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

Abstract

A carpet is a metric space homeomorphic to the Sierpinski carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.

v1: 42 pages, 11 figures. v2: 42 pages, 10 figures. Improved exposition

References in corpus (2)

• A Sierpiński carpet with the co-Hopfian property
• Planar relative Schottky sets and quasisymmetric maps

Cited by in corpus (3)

• Local Dirichlet forms, Hodge theory, and the Navier-Stokes equations on topologically one-dimensional fractals
• Curvewise characterizations of minimal upper gradients and the construction of a Sobolev differential
• Almost uniform domains and Poincaré inequalities