Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917694815600640 |
|---|---|
| author | Mei, Xinqun Weng, Liangjun |
| author_facet | Mei, Xinqun Weng, Liangjun |
| contents | In this article, we first introduce the quermassintegrals for compact hypersurfaces with capillary boundaries in hyperbolic space from a variational viewpoint, and then we solve an isoperimetric type problem in hyperbolic space. By constructing a new locally constrained inverse curvature flow, we obtain the Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in hyperbolic space. This generalizes a theorem of Brendle-Guan-Li \cite{BGL} for convex closed hypersurfaces in hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space Mei, Xinqun Weng, Liangjun Differential Geometry Analysis of PDEs Primary 53C21, 35B40, Secondary 52A40, 53E40, 35K96 In this article, we first introduce the quermassintegrals for compact hypersurfaces with capillary boundaries in hyperbolic space from a variational viewpoint, and then we solve an isoperimetric type problem in hyperbolic space. By constructing a new locally constrained inverse curvature flow, we obtain the Alexandrov-Fenchel inequalities for convex capillary hypersurfaces in hyperbolic space. This generalizes a theorem of Brendle-Guan-Li \cite{BGL} for convex closed hypersurfaces in hyperbolic space. |
| title | Alexandrov-Fenchel inequalities for capillary hypersurfaces in hyperbolic space |
| topic | Differential Geometry Analysis of PDEs Primary 53C21, 35B40, Secondary 52A40, 53E40, 35K96 |
| url | https://arxiv.org/abs/2406.07304 |