A mean curvature type flow with capillary boundary in a horoball in hyperbolic space
Differential Geometry
2025-05-07 v1
Abstract
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.
Cite
@article{arxiv.2405.08446,
title = {A mean curvature type flow with capillary boundary in a horoball in hyperbolic space},
author = {Jinyu Guo},
journal= {arXiv preprint arXiv:2405.08446},
year = {2025}
}
Comments
18 pages, 1 figure