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arXiv · 2401.08028

Improved regularity for minimizing capillary hypersurfaces

Otis Chodosh·Nick Edelen·Chao Li
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Abstract

We give improved estimates for the size of the singular set of minimizing capillary hypersurfaces: the singular set is always of codimension at least $4$, and this estimate improves if the capillary angle is close to $0$, $\frac{\pi}{2}$, or $\pi$. For capillary angles that are close to $0$ or $\pi$, our analysis is based on a rigorous connection between the capillary problem and the one-phase Bernoulli problem.

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Otis Chodosh, Nick Edelen, Chao Li. 2024-01-16. Improved regularity for minimizing capillary hypersurfaces. https://arxiv.org/abs/2401.08028

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