A mean curvature type flow with capillary boundary in a horoball in hyperbolic space
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909601805369344 |
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| author | Guo, Jinyu |
| author_facet | Guo, Jinyu |
| contents | In this paper, we study a mean curvature type flow with capillary boundary in a horoball in hyperbolic space. Our flow preserves the volume of the bounded domain enclosed by the hypersurface and monotonically decreases the energy functional. We show that it has the long time existence and converges to a truncated umbilical hypersurface in hyperbolic space. As an application, we solve an isoperimetric type problem for hypersurfaces with capillary boundary in a horoball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A mean curvature type flow with capillary boundary in a horoball in hyperbolic space Guo, Jinyu Differential Geometry In this paper, we study a mean curvature type flow with capillary boundary in a horoball in hyperbolic space. Our flow preserves the volume of the bounded domain enclosed by the hypersurface and monotonically decreases the energy functional. We show that it has the long time existence and converges to a truncated umbilical hypersurface in hyperbolic space. As an application, we solve an isoperimetric type problem for hypersurfaces with capillary boundary in a horoball. |
| title | A mean curvature type flow with capillary boundary in a horoball in hyperbolic space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2405.08446 |