Characterizations of monotonicity of vector fields on metric measure spaces (Q1800855)

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English	Characterizations of monotonicity of vector fields on metric measure spaces	scientific article

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scholarly article

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Characterizations of monotonicity of vector fields on metric measure spaces (English)

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Calculus of Variations and Partial Differential Equations

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publication date

26 October 2018

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full work available at URL

https://arxiv.org/abs/1710.07953

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zbMATH Keywords

metric measure spaces

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curvature

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MaRDI profile type

MaRDI publication profile

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Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

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Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure

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Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

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Metric measure spaces with Riemannian Ricci curvature bounded from below

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Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds

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On the Bakry-Émery condition, the gradient estimates and the local-to-global property of \(\mathrm{RCD}^*(K,N)\) metric measure spaces

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Weak and strong convergence of derivations and stability of flows with respect to MGH convergence

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Well-posedness of Lagrangian flows and continuity equations in metric measure spaces

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Localization and tensorization properties of the curvature-dimension condition for metric measure spaces

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Lower bounds on Ricci curvature and the almost rigidity of warped products

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On the structure of spaces with Ricci curvature bounded below. I

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On the structure of spaces with Ricci curvature bounded below. II

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On the structure of spaces with Ricci curvature bounded below. III

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The splitting theorem for manifolds of nonnegative Ricci curvature

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From volume cone to metric cone in the nonsmooth setting

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The heat equation on manifolds as a gradient flow in the Wasserstein space

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On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces

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On the differential structure of metric measure spaces and applications

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Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below

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The continuity equation on metric measure spaces

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Sobolev spaces on warped products

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Recognizing the flat torus among \(\mathsf{RCD}^*(0,N)\) spaces via the study of the first cohomology group

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Second order differentiation formula on \(\mathsf{RCD}(K,N)\) spaces

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Ricci tensor on \(\mathrm{RCD}^\ast(K,N)\) spaces

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On the volume measure of non-smooth spaces with Ricci curvature bounded below

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Obata's rigidity theorem for metric measure spaces

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Duality on gradient estimates and Wasserstein controls

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Neumann heat flow and gradient flow for the entropy on non-convex domains

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Characterization of absolutely continuous curves in Wasserstein spaces

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Ricci curvature for metric-measure spaces via optimal transport

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Non-branching geodesics and optimal maps in strong \(CD(K,\infty)\)-spaces

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Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces

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Newtonian spaces: An extension of Sobolev spaces to metric measure spaces

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On the geometry of metric measure spaces. I

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On the geometry of metric measure spaces. II

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Optimal Transport

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Transport inequalities, gradient estimates, entropy and Ricci curvature

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1007/S00526-018-1388-9

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Sitelinks

Mathematics(1 entry)

mardi Publication:1800855

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