English

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}
}