Weiss monotonicity and capillary hypersurfaces
Analysis of PDEs
2025-06-04 v1 Differential Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.2506.02146,
title = {Weiss monotonicity and capillary hypersurfaces},
author = {Otis Chodosh and Nick Edelen and Chao Li},
journal= {arXiv preprint arXiv:2506.02146},
year = {2025}
}