Sectional curvature and matrix displacement convexity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914061187284992 |
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| author | Aishwarya, Gautam Rotem, Liran Shenfeld, Yair |
| author_facet | Aishwarya, Gautam Rotem, Liran Shenfeld, Yair |
| contents | We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy functional is matrix displacement convex. As an application we obtain intrinsic dimensional evolution variational inequalities, and the corresponding Wasserstein contraction along heat flows, which improve on their dimensional counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sectional curvature and matrix displacement convexity Aishwarya, Gautam Rotem, Liran Shenfeld, Yair Differential Geometry Analysis of PDEs Probability 35K05, 58J35, 53C21, 49Q22 We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy functional is matrix displacement convex. As an application we obtain intrinsic dimensional evolution variational inequalities, and the corresponding Wasserstein contraction along heat flows, which improve on their dimensional counterparts. |
| title | Sectional curvature and matrix displacement convexity |
| topic | Differential Geometry Analysis of PDEs Probability 35K05, 58J35, 53C21, 49Q22 |
| url | https://arxiv.org/abs/2509.23399 |