[图书][B] Optimal transport: old and new
C Villani - 2009 - Springer
At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …
John Mather launched a revolution in the venerable field of optimal transport founded by G …
[图书][B] On the differential structure of metric measure spaces and applications
N Gigli - 2015 - ams.org
The main goals of this paper are:(i) To develop an abstract differential calculus on metric
measure spaces by investigating the duality relations between differentials and gradients of …
measure spaces by investigating the duality relations between differentials and gradients of …
Finsler interpolation inequalities
S Ohta - Calculus of Variations and Partial Differential …, 2009 - Springer
Abstract We extend Cordero-Erausquin et al.'s Riemannian Borell–Brascamp–Lieb
inequality to Finsler manifolds. Among applications, we establish the equivalence between …
inequality to Finsler manifolds. Among applications, we establish the equivalence between …
Localization and tensorization properties of the curvature-dimension condition for metric measure spaces
K Bacher, KT Sturm - Journal of Functional Analysis, 2010 - Elsevier
This paper is devoted to the analysis of metric measure spaces satisfying locally the
curvature-dimension condition CD (K, N) introduced by the second author and also studied …
curvature-dimension condition CD (K, N) introduced by the second author and also studied …
[HTML][HTML] Cones over metric measure spaces and the maximal diameter theorem
C Ketterer - Journal de Mathématiques Pures et Appliquées, 2015 - Elsevier
The main result of this article states that the (K, N)-cone over some metric measure space
satisfies the reduced Riemannian curvature-dimension condition RCD⁎(KN, N+ 1) if and …
satisfies the reduced Riemannian curvature-dimension condition RCD⁎(KN, N+ 1) if and …
New formulas for the Laplacian of distance functions and applications
F Cavalletti, A Mondino - Analysis & PDE, 2020 - msp.org
The goal of the paper is to prove an exact representation formula for the Laplacian of the
distance (and more generally for an arbitrary 1-Lipschitz function) in the framework of metric …
distance (and more generally for an arbitrary 1-Lipschitz function) in the framework of metric …
Ricci curvature on Alexandrov spaces and rigidity theorems
HC Zhang, XP Zhu - arXiv preprint arXiv:0912.3190, 2009 - arxiv.org
arXiv:0912.3190v4 [math.DG] 26 Sep 2010 Page 1 arXiv:0912.3190v4 [math.DG] 26 Sep 2010
RICCI CURVATURE ON ALEXANDROV SPACES AND RIGIDITY THEOREMS HUI-CHUN …
RICCI CURVATURE ON ALEXANDROV SPACES AND RIGIDITY THEOREMS HUI-CHUN …
Sub-Riemannian interpolation inequalities
D Barilari, L Rizzi - Inventiones mathematicae, 2019 - Springer
We prove that ideal sub-Riemannian manifolds (ie, admitting no non-trivial abnormal
minimizers) support interpolation inequalities for optimal transport. A key role is played by …
minimizers) support interpolation inequalities for optimal transport. A key role is played by …
Gradient flows on Wasserstein spaces over compact Alexandrov spaces
S Ohta - American journal of mathematics, 2009 - muse.jhu.edu
We establish the existence of Euclidean tangent cones on Wasserstein spaces over
compact Alexandrov spaces of curvature bounded below. By using this Riemannian …
compact Alexandrov spaces of curvature bounded below. By using this Riemannian …
Obata's rigidity theorem for metric measure spaces
C Ketterer - Analysis and Geometry in Metric Spaces, 2015 - degruyter.com
We prove Obata's rigidity theorem for metric measure spaces that satisfy a Riemannian
curvaturedimension condition. Additionally, we show that a lower bound K for the …
curvaturedimension condition. Additionally, we show that a lower bound K for the …