Regularity of minimal surfaces with capillary boundary conditions

2024/05/31 by Luigi De Masi, Nick Edelen, De Masi, Luigi +5 · 5 citations
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2405.20796

Abstract

We prove ε-regularity theorems for varifolds with capillary boundary condition in a Riemannian manifold. These varifolds were first introduced by Kagaya-Tonegawa \citeKaTo. We establish a uniform first variation control for all such varifolds (and free-boundary varifolds generally) satisfying a sharp density bound and prove that if a capillary varifold has bounded mean curvature and is close to a capillary half-plane with angle not equal to \tfracπ2, then it coincides with a C^1,α properly embedded hypersurface. We apply our theorem to deduce regularity at a generic point along the boundary in the region where the density is strictly less than 1.

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