Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909500919775232 |
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| author | Sinestrari, Carlo Weng, Liangjun |
| author_facet | Sinestrari, Carlo Weng, Liangjun |
| contents | In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hypersurface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as $t \to +\infty$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02722 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow Sinestrari, Carlo Weng, Liangjun Differential Geometry Analysis of PDEs 53E10 In this paper, we introduce a volume- or area-preserving curvature flow for hypersurfaces with capillary boundary in the half-space, with speed given by a positive power of the mean curvature with a non-local averaging term. We demonstrate that for any convex initial hypersurface with a capillary boundary, the flow exists for all time and smoothly converges to a spherical cap as $t \to +\infty$ |
| title | Hypersurfaces with capillary boundary evolving by volume preserving power mean curvature flow |
| topic | Differential Geometry Analysis of PDEs 53E10 |
| url | https://arxiv.org/abs/2405.02722 |