A mean curvature type flow with capillary boundary in a unit ball
Differential Geometry
2026-02-19 v2 Analysis of PDEs
Abstract
In this paper, we study a mean curvature type flow with capillary boundary in the unit ball. Our flow preserves the volume of the bounded domain enclosed by the hypersurface, and monotonically decreases an energy functional . We show that it has the longtime existence and subconverges to spherical caps. As an application, we solve an isoperimetric problem for hypersurfaces with capillary boundary.
Keywords
Cite
@article{arxiv.2001.03118,
title = {A mean curvature type flow with capillary boundary in a unit ball},
author = {Guofang Wang and Liangjun Weng},
journal= {arXiv preprint arXiv:2001.03118},
year = {2026}
}
Comments
28 pages with some revisions: typos are corrected, rewrite Section 2.2, notations are unified and presentations are simplified. To appear in Calc. Var. Partial Differential Equations