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Min-max construction of minimal surfaces with a fixed angle at the boundary

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arxiv 2111.09913 v1 pith:UDLMIVQ4 submitted 2021-11-18 math.DG math.AP

Luigi De Masi , Guido De Philippis This is my paper · ORCID
classification math.DGmath.AP
keywords angleboundaryconstructionfixedmathcalmin-maxminimalsurfaces
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abstract

We prove the existence of minimal surfaces in a bounded convex subset of $\mathbb R^3$, $\mathcal M$, intersecting the boundary of $\mathcal M$ with a fixed contact angle. The proof is based on a min-max construction in the spirit of Almgren-Pitts for the capillarity functional.

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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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