Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon-Nikodym property
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Publication:2655447
DOI10.1007/s00039-009-0030-6zbMath1200.58007arXiv0808.3249OpenAlexW2963543118MaRDI QIDQ2655447
Publication date: 25 January 2010
Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0808.3249
Banach spacedoubling measuremetric measure spaceLipschitz functionRadon-Nikodýmminimal upper gradient
Differentiation theory (Gateaux, Fréchet, etc.) on manifolds (58C20) Analysis on metric spaces (30L99) Geometric embeddings of metric spaces (30L05)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- New classes of \(L_ p-\)spaces
- Differentiability of Lipschitz functions on metric measure spaces
- Lectures on analysis on metric spaces
- The large scale geometry in nilpotent Lie groups
- Sobolev classes of Banach space-valued functions and quasiconformal mappings
- Geometric aspects of convex sets with the Radon-Nikodym property
- Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
- Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
- Generalized differentiation and bi-Lipschitz nonembedding in \(L^{1}\)
- Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
- Rectifiable Metric Spaces: Local Structure and Regularity of the Hausdorff Measure
- From local to global in quasiconformal structures.
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