An inverse problem in optimal transport on closed Riemannian manifolds

Jian Zhai; Kelvin Shuangjian Zhang

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arXiv · 2511.15037

An inverse problem in optimal transport on closed Riemannian manifolds

Jian Zhai·Kelvin Shuangjian Zhang

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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.

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Jian Zhai, Kelvin Shuangjian Zhang. 2025-11-19. An inverse problem in optimal transport on closed Riemannian manifolds. https://arxiv.org/abs/2511.15037

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