Stability of optimal transport on metric measure spaces

arXiv (Cornell University) 2026 Preprint Open access

Read full text
Authors: Bang-Xian Han, Zhuo-Nan Zhu
DOI: 10.48550/arxiv.2602.19175
Cited by: 0

Abstract

We prove a quantitative stability of Kantorovich potentials on metric measure spaces with lower Ricci curvature bound, thereby confirming a recent conjecture of Kitagawa, Letrouit and Mérigot. Our proof, which employs the heat kernel-regularized $c$-transform, does not rely on linear structure or sectional curvature bounds. As a corollary, we get a quantitative stability of optimal transport maps on Alexandrov spaces with lower curvature bound.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Advanced Differential Geometry Research Mathematical Inequalities and Applications

Publication details

Journal / source
arXiv (Cornell University)
Publication date
22 February 2026
Language
EN
Document type
Preprint