Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909192713928704 |
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| author | Ishige, Kazuhiro Takatsu, Asuka Tokunaga, Haruto |
| author_facet | Ishige, Kazuhiro Takatsu, Asuka Tokunaga, Haruto |
| contents | We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_03982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds Ishige, Kazuhiro Takatsu, Asuka Tokunaga, Haruto Analysis of PDEs Differential Geometry 35E10, 58J35 We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain. |
| title | Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds |
| topic | Analysis of PDEs Differential Geometry 35E10, 58J35 |
| url | https://arxiv.org/abs/2405.03982 |