A Minkowski-type inequality for capillary hypersurfaces in a half-space
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929439169839104 |
|---|---|
| author | Wang, Guofang Weng, Liangjun Xia, Chao |
| author_facet | Wang, Guofang Weng, Liangjun Xia, Chao |
| contents | In this article, we investigate a flow of inverse mean curvature type for capillary hypersurfaces in the half-space. We establish the global existence of solutions for this flow and demonstrate that it converges smoothly to a spherical cap as time tends to infinity. As a result, we derive a new Minkowski-type inequality for star-shaped and mean convex capillary hypersurfaces for the whole range of contact angle $θ\in (0,π)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13516 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Minkowski-type inequality for capillary hypersurfaces in a half-space Wang, Guofang Weng, Liangjun Xia, Chao Analysis of PDEs Differential Geometry 53E10 (Primary) 53C21, 35K93, 53C24 (Secondary) In this article, we investigate a flow of inverse mean curvature type for capillary hypersurfaces in the half-space. We establish the global existence of solutions for this flow and demonstrate that it converges smoothly to a spherical cap as time tends to infinity. As a result, we derive a new Minkowski-type inequality for star-shaped and mean convex capillary hypersurfaces for the whole range of contact angle $θ\in (0,π)$. |
| title | A Minkowski-type inequality for capillary hypersurfaces in a half-space |
| topic | Analysis of PDEs Differential Geometry 53E10 (Primary) 53C21, 35K93, 53C24 (Secondary) |
| url | https://arxiv.org/abs/2209.13516 |