The quermassintegral preserving mean curvature flow in the sphere
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866915034244841472 |
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| author | Cabezas-Rivas, Esther Scheuer, Julian |
| author_facet | Cabezas-Rivas, Esther Scheuer, Julian |
| contents | We introduce a mean curvature flow with global term of convex hypersurfaces in the sphere, for which the global term can be chosen to keep any quermassintegral fixed. Then, starting from a strictly convex initial hypersurface, we prove that the flow exists for all times and converges smoothly to a geodesic sphere. This provides a workaround to an issue present in the volume preserving mean curvature flow in the sphere introduced by Huisken in 1987. We also classify solutions for some constant curvature type equations in space forms, as well as solitons in the sphere and in the upper branch of the De Sitter space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_17040 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The quermassintegral preserving mean curvature flow in the sphere Cabezas-Rivas, Esther Scheuer, Julian Differential Geometry Analysis of PDEs 53E10, 53C21 We introduce a mean curvature flow with global term of convex hypersurfaces in the sphere, for which the global term can be chosen to keep any quermassintegral fixed. Then, starting from a strictly convex initial hypersurface, we prove that the flow exists for all times and converges smoothly to a geodesic sphere. This provides a workaround to an issue present in the volume preserving mean curvature flow in the sphere introduced by Huisken in 1987. We also classify solutions for some constant curvature type equations in space forms, as well as solitons in the sphere and in the upper branch of the De Sitter space. |
| title | The quermassintegral preserving mean curvature flow in the sphere |
| topic | Differential Geometry Analysis of PDEs 53E10, 53C21 |
| url | https://arxiv.org/abs/2211.17040 |