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Main Author: Huang, Zhengyao
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2603.18935
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author Huang, Zhengyao
author_facet Huang, Zhengyao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_18935
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature
Huang, Zhengyao
Analysis of PDEs
Optimization and Control
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.
title A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature
topic Analysis of PDEs
Optimization and Control
url https://arxiv.org/abs/2603.18935