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Improved regularity for minimizing capillary hypersurfaces

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arxiv 2401.08028 v3 pith:6RZUPR7D submitted 2024-01-16 math.DG math.AP

Otis Chodosh , Nick Edelen , Chao Li This is my paper · ORCID
classification math.DGmath.AP
keywords capillaryclosehypersurfacesimprovedminimizingproblemsingularalways
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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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  1. Some remarks on singular capillary cones with free boundary

    math.DG 2025-02 conditional novelty 7.0 of 10

    Minimizing capillary cones are flat in dimension 4 when the free-boundary mean curvature has one sign, and axially symmetric ones are flat up to dimension 6.

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