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arXiv · 2603.18935

A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature

Zhengyao Huang
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Abstract

In this paper, we study Monge's problem on Riemannian manifolds $(M, g)$ with positive sectional curvature. Assuming that the source and target measures are absolutely continuous with respect to the Riemannian volume measure, we generalize a variational method from the Euclidean setting to establish the existence of a transport density and an explicit disintegration of measures along optimal rays. These results extend the approach of Bianchini-Caravenna to the Riemannian context.

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Zhengyao Huang. 2026-03-19. A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature. https://arxiv.org/abs/2603.18935

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