Gradient flows on Wasserstein spaces over compact Alexandrov spaces

By Shin-ichi Ohta. 2009

97 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/76debbf6feece8f81dc487eef65997c1040d1841

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In Applied Mathematics

In Astronomy and Astrophysics

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Citations in the corpus

On the inverse implication of Brenier-Mccann theorems and the structure of (P 2 (M),W 2 ) (2011, methodology): “of [27], where it was firstly proven the existence of the limit lim ε↓0 W2(μεt, νεs) ε =: f(t, s), and then that the value of t(2)|μ̇t| 2 + s(2)|ν̇s| − f (2)(t, s) 2ts ,”
Geometry and Analysis of Dirichlet forms (2012, background): “We begin with a variant of the dual formula established in [28, Theorem 2.2], which is closely related to the coarse Ricci curvature of Ollivier [33].”
Gradient flows and diffusion semigroups in metric spaces under lower curvature bounds (2007, methodology): “Besides Alexandrov spaces (considered by a completely different method in the unpublished [9] and, when X is compact and positively curved, in the recent [8]), our approach covers more general situations, as the Wasserstein space P2(X), when the Riemannian manifold X has points with negative section”
Barycenters in Alexandrov spaces of curvature bounded below (2012, background): “Nonetheless, we see in [ Oh3 , Theorem 3.6] that the angle between two geodesics in the”
Duality on gradient estimates and Wasserstein controls (2009, background): “Under this condition, the existence of a heat flow and an L(2)-Wasserstein control follow in some cases beyond Riemannian manifolds [29, 32] (see [14, 36] for the case on a Riemannian manifold).”
Gradient flows and Evolution Variational Inequalities in metric spaces. I: Structural properties (2018, unknown): “In [70] we will generalize this result to cover arbitrary Alexandrov spaces and even more general cases, characterized by a new geometric property, weaker than the Alexandrov one, based on a local angle condition between geodesics and on the semi-concavity of the squared distance [82, 35] (see also ”