An 𝑛-dimensional space that admits a Poincaré inequality but has no manifold points

DOI10.1090/S0002-9939-00-05453-8zbMath0954.43005MaRDI QIDQ4505893

No author found.

Publication date: 3 October 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Poincaré inequalityAhlfors regularity conditionmanifold points

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Length, area, volume, other geometric measure theory (28A75)

Related Items

Modulus and Poincaré inequalities on non-self-similar Sierpiński carpets ⋮ Functions of bounded variation on ``good metric spaces ⋮ The Poincaré inequality does not improve with blow-up ⋮ Metric and geometric quasiconformality in Ahlfors regular Loewner spaces ⋮ Poincaré inequality for abstract spaces ⋮ Sobolev Mappings between Manifolds and Metric Spaces ⋮ Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces ⋮ A differentiable structure for metric measure spaces ⋮ Lipschitz algebras and derivations. II: Exterior differentiation ⋮ Sobolev classes of Banach space-valued functions and quasiconformal mappings

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
• Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings