A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature

Zhengyao Huang

A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature

Analysis of PDEs 2026-03-20 v1 Optimization and Control

Authors: Zhengyao Huang

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.

Keywords

Monge problem Riemannian manifolds Sudakov decomposition optimal transport sectional curvature

Cite

@article{arxiv.2603.18935,
  title  = {A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature},
  author = {Zhengyao Huang},
  journal= {arXiv preprint arXiv:2603.18935},
  year   = {2026}
}

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