Min-max construction of minimal surfaces with a fixed angle at the boundary (2111.09913v1)

Published 18 Nov 2021 in math.DG and math.AP

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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