Rigidity of derivations in the plane and in metric measure spaces

zbMath1295.46030arXiv1110.4282MaRDI QIDQ2452314

Jasun Gong

Publication date: 2 June 2014

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.4282

zbMATH Keywords

Poincaré inequalityLipschitz algebraderivationCheeger's conjectureWeaver theory

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (5)

On the singular part of measures constrained by linear PDEs and applications ⋮ Metric currents and Alberti representations ⋮ Sierpinski-type fractals are differentiably trivial ⋮ Structure of measures in Lipschitz differentiability spaces ⋮ Derivations and Alberti representations

Cites Work

• On embedding uniform and topological spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Lectures on analysis on metric spaces
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Lipschitz algebras and derivations. II: Exterior differentiation
• Two problems on doubling measures
• Lipschitz algebras and derivations of von Neumann algebras
• Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
• Nonsmooth calculus
• A doubling measure on $\mathbb {R}^d$ can charge a rectifiable curve
• Extensions of Hardy spaces and their use in analysis
• Hausdorff dimension and doubling measures on metric spaces
• Extension of range of functions
• Measurable differentiable structures and the Poincare inequality
• Admissible measures in one dimension

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