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<p>This paper approaches the smoothness of the optimal transport map on Riemannian products manifolds. By classical continuity method, we give an alternative proof of the smoothness of the optimal transport map on Riemannian products of the round spheres. In addition, we also prove that the smoothness of the optimal transport map is not stable in Riemannian products of round spheres.</p>

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Smoothness of the Optimal Transport Map on Riemannian Products of Spheres

  • 期刊论文

  • 发表日期：

    2025年5月13日

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  • Jian Ye

摘要

This paper approaches the smoothness of the optimal transport map on Riemannian products manifolds. By classical continuity method, we give an alternative proof of the smoothness of the optimal transport map on Riemannian products of the round spheres. In addition, we also prove that the smoothness of the optimal transport map is not stable in Riemannian products of round spheres.