A fully nonlinear locally constrained curvature flow for capillary hypersurface
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909501059235840 |
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| author | Mei, Xinqun Weng, Liangjun |
| author_facet | Mei, Xinqun Weng, Liangjun |
| contents | In this article, we study a locally constrained fully nonlinear curvature flow for convex capillary hypersurfaces in half-space. We prove that the flow preserves the convexity, exists for all time, and converges smoothly to a spherical cap. This can be viewed as the fully nonlinear counterpart of the result in \cite{MWW}. As a byproduct, a high-order capillary isoperimetric ratio (1.6) evolves monotonically along this flow, which yields a class of the Alexandrov-Fenchel inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13815 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fully nonlinear locally constrained curvature flow for capillary hypersurface Mei, Xinqun Weng, Liangjun Analysis of PDEs In this article, we study a locally constrained fully nonlinear curvature flow for convex capillary hypersurfaces in half-space. We prove that the flow preserves the convexity, exists for all time, and converges smoothly to a spherical cap. This can be viewed as the fully nonlinear counterpart of the result in \cite{MWW}. As a byproduct, a high-order capillary isoperimetric ratio (1.6) evolves monotonically along this flow, which yields a class of the Alexandrov-Fenchel inequalities. |
| title | A fully nonlinear locally constrained curvature flow for capillary hypersurface |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.13815 |