On the geometry of geodesics in discrete optimal transport

被引：8

作者：

Erbar, Matthias ^{[1
]}

Maas, Jan ^{[2
]}

Wirth, Melchior ^{[3
]}

机构：

[1] Univ Bonn, Inst Angew Math, Endenicher Allee 60, D-53115 Bonn, Germany

[2] Inst Sci & Technol Austria IST Austria, Campus 1, A-3400 Klosterneuburg, Austria

[3] Friedrich Schiller Univ Jena, Inst Math, D-07737 Jena, Germany

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2019年 / 58卷 / 01期

基金：

奥地利科学基金会; 欧洲研究理事会;

关键词：

HAMILTON-JACOBI EQUATIONS; METRIC-MEASURE-SPACES; RICCI CURVATURE; ENTROPY;

D O I：

10.1007/s00526-018-1456-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the space of probability measures on a discrete set X, endowed with a dynamical optimal transport metric. Given two probability measures supported in a subset Y. X, it is natural to ask whether they can be connected by a constant speed geodesic with support in Y at all times. Our main result answers this question affirmatively, under a suitable geometric condition on Y introduced in this paper. The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi equations, which is of independent interest.

引用

页数：19

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