A first-order condition for the independence on \(p\) of weak gradients
DOI10.1016/j.jfa.2022.109686zbMath1503.53087arXiv2112.12849OpenAlexW4293879698MaRDI QIDQ2172482
Francesco Nobili, Nicola Gigli
Publication date: 15 September 2022
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.12849
Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Differential geometric aspects of statistical manifolds and information geometry (53B12) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)
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Cites Work
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- Independence on \(p\) of weak upper gradients on \(\mathsf{RCD}\) spaces
- Density of Lipschitz functions and equivalence of weak gradients in metric measure spaces
- Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
- Nonlinear potential theory on metric spaces
- A characterization of Newtonian functions with zero boundary values
- Existence and uniqueness of optimal transport maps
- Differentiability of Lipschitz functions on metric measure spaces
- Modulus and the Poincaré inequality on metric measure spaces
- Lecture notes on differential calculus on \(\mathsf{RCD}\) spaces
- Recognizing the flat torus among \(\mathsf{RCD}^*(0,N)\) spaces via the study of the first cohomology group
- Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
- Sobolev spaces on an arbitrary metric space
- Korevaar-Schoen's energy on strongly rectifiable spaces
- Lectures on nonsmooth differential geometry
- Transport maps, non-branching sets of geodesics and measure rigidity
- Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
- Metric measure spaces with Riemannian Ricci curvature bounded from below
- On the measure contraction property of metric measure spaces
- On local Poincaré via transportation
- On the geometry of metric measure spaces. I
- On the geometry of metric measure spaces. II
- Non-branching geodesics and optimal maps in strong \(CD(K,\infty)\)-spaces
- \((K,N)\)-convexity and the curvature-dimension condition for negative \(N\)
- On the differential structure of metric measure spaces and applications
- The $p$-weak gradient depends on $p$
- Convergence of pointed non-compact metric measure spaces and stability of Ricci curvature bounds and heat flows
- Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
- Independence of synthetic curvature dimension conditions on transport distance exponent
- Testing the Sobolev property with a single test plan
- Optimal maps in essentially non-branching spaces
- Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
- Optimal Transport
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