Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces

被引：20
作者：
Ambrosio, Luigi [1 ]
Erbar, Matthias [2 ]
Savare, Giuseppe [3 ]
机构：
[1] Scuola Normale Super Pisa, Pisa, Italy
[2] Univ Bonn, Bonn, Germany
[3] Univ Pavia, I-27100 Pavia, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2016年 / 137卷
基金：
欧洲研究理事会;
关键词：
Optimal transport; Evolution variational inequality; Heat flow; METRIC MEASURE-SPACES; RADEMACHERS THEOREM; DIRICHLET FORMS; GEOMETRY; FLOWS;
D O I：
10.1016/j.na.2015.12.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce the setting of extended metric-topological measure spaces as a general "Wiener like" framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a brief review of optimal transport tools for general Radon measures, we discuss the notions of the Cheeger energy, of the Radon measures concentrated on absolutely continuous curves, and of the induced "dynamic transport distances". We study their main properties and their links with the theory of Dirichlet forms and the Bakry-Emery curvature condition, in particular concerning the contractivity properties and the EVI formulation of the induced Heat semigroup. (c) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：77 / 134
页数：58
相关论文
共 47 条
  • [1] Analysis and geometry on configuration spaces
    Albeverio, S
    Kondratiev, YG
    Rockner, M
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1998, 154 (02) : 444 - 500
  • [2] Ambrosio L., 2008, Gradient flows: in metric spaces and in the space of probability measures, V2, P334
  • [3] Ambrosio L., 2013, J GEOM ANAL IN PRESS, P1
  • [4] Ambrosio L., UNPUB
  • [5] Ambrosio L, 2015, ADV STU P M, V67, P1
  • [6] WELL-POSEDNESS OF LAGRANGIAN FLOWS AND CONTINUITY EQUATIONS IN METRIC MEASURE SPACES
    Ambrosio, Luigi
    Trevisan, Dario
    [J]. ANALYSIS & PDE, 2014, 7 (05): : 1179 - 1234
  • [7] METRIC MEASURE SPACES WITH RIEMANNIAN RICCI CURVATURE BOUNDED FROM BELOW
    Ambrosio, Luigi
    Gigli, Nicola
    Savare, Giuseppe
    [J]. DUKE MATHEMATICAL JOURNAL, 2014, 163 (07) : 1405 - 1490
  • [8] Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
    Ambrosio, Luigi
    Gigli, Nicola
    Savare, Giuseppe
    [J]. INVENTIONES MATHEMATICAE, 2014, 195 (02) : 289 - 391
  • [9] BAKRY-EMERY CURVATURE-DIMENSION CONDITION AND RIEMANNIAN RICCI CURVATURE BOUNDS
    Ambrsio, Luigi
    Gigli, Nicola
    Savare, Giuseppe
    [J]. ANNALS OF PROBABILITY, 2015, 43 (01) : 339 - 404
  • [10] [Anonymous], 1991, DEGRUYTER STUDIES MA
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