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arXiv · 2506.02146

Weiss monotonicity and capillary hypersurfaces

Otis Chodosh·Nick Edelen·Chao Li
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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.

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Otis Chodosh, Nick Edelen, Chao Li. 2025-06-02. Weiss monotonicity and capillary hypersurfaces. https://arxiv.org/abs/2506.02146

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