A Sudakov Decomposition in Riemannian Manifolds with Positive Curvature
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908901352407040 |
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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 |