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arXiv · 2602.19175

Stability of optimal transport on metric measure spaces

Bang-Xian Han·Zhuo-Nan Zhu
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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 M\'erigot. 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.

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Bang-Xian Han, Zhuo-Nan Zhu. 2026-02-22. Stability of optimal transport on metric measure spaces. https://arxiv.org/abs/2602.19175

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