An inverse problem in optimal transport on closed Riemannian manifolds
Analysis of PDEs
2025-11-20 v1
Abstract
We consider the problem of recovering the Riemannian metric on a compact closed manifold from the optimal transport maps when the underlying cost function is the squared Riemann distance. We show that the metric can be uniquely determined up to a multiplicative constant.
Keywords
Cite
@article{arxiv.2511.15037,
title = {An inverse problem in optimal transport on closed Riemannian manifolds},
author = {Jian Zhai and Kelvin Shuangjian Zhang},
journal= {arXiv preprint arXiv:2511.15037},
year = {2025}
}