A boundary maximum principle for stationary pairs of varifolds with fixed contact angle

TL;DR

This paper proves a boundary maximum principle for stationary pairs of varifolds with a fixed contact angle in compact Riemannian manifolds, advancing understanding of geometric variational problems with boundary conditions.

Contribution

It introduces a boundary maximum principle applicable to stationary varifold pairs with fixed contact angles in Riemannian manifolds, extending previous boundary regularity results.

Findings

Established a boundary maximum principle for stationary varifold pairs

Applicable to manifolds with smooth boundary

Generalizes previous boundary regularity results

Abstract

In this note, we establish a boundary maximum principle for a class of stationary pairs of varifolds satisfying a fixed contact angle condition in any compact Riemannian manifold with smooth boundary.