A fixed contact angle condition for varifolds

TL;DR

This paper introduces a generalized fixed contact angle condition for varifolds, extending boundary behavior analysis and establishing a boundary monotonicity formula, generalizing previous Neumann boundary condition results.

Contribution

It defines a new boundary condition for varifolds and proves a boundary monotonicity formula, broadening the understanding of boundary behaviors in geometric measure theory.

Findings

Established a generalized fixed contact angle condition for varifolds.

Proved a boundary monotonicity formula under this new condition.

Generalized previous results for Neumann boundary conditions.

Abstract

We define a generalized fixed contact angle condition for $n$-varifold and establish a boundary monotonicity formula. The results are natural generalizations of those for the Neumann boundary condition considered by Gr\"uter-Jost.