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

Guido De Philippis; Luigi De Masi

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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

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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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