Weiss monotonicity and capillary hypersurfaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918044197978112 |
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| author | Chodosh, Otis Edelen, Nick Li, Chao |
| author_facet | Chodosh, Otis Edelen, Nick Li, Chao |
| contents | Previous work of the authors established the rigorous limiting behavior of minimizing capillary surfaces to minimizers of the Alt--Caffarelli functional as the capillary angle tends to zero. We prove here that in this limit, the capillary area-density converges to the Weiss energy density. We apply this to obtain angle-independent curvature estimates and regularity results for capillary minimizers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02146 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weiss monotonicity and capillary hypersurfaces Chodosh, Otis Edelen, Nick Li, Chao Analysis of PDEs Differential Geometry Previous work of the authors established the rigorous limiting behavior of minimizing capillary surfaces to minimizers of the Alt--Caffarelli functional as the capillary angle tends to zero. We prove here that in this limit, the capillary area-density converges to the Weiss energy density. We apply this to obtain angle-independent curvature estimates and regularity results for capillary minimizers. |
| title | Weiss monotonicity and capillary hypersurfaces |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2506.02146 |