Varifolds with capillary boundary
Differential Geometry
2025-03-26 v1
Abstract
In this paper we introduce and study a new class of varifolds in of arbitrary dimensions and co-dimensions, which satisfy a Neumann-type boundary condition characterizing capillarity. The key idea is to introduce a Radon measure on a subspace of the trivial Grassmannian bundle over the supporting hypersurface as a generalized boundary with prescribed angle, which plays a role as a measure-theoretic capillary boundary. We show several structural properties, monotonicity inequality, boundary rectifiability, classification of tangent cones, and integral compactness for such varifolds under reasonable conditions. This Neumann-type boundary condition fits very well in the context of curvature varifold and Brakke flow, which we also discuss.
Cite
@article{arxiv.2503.19052,
title = {Varifolds with capillary boundary},
author = {Guofang Wang and Xuwen Zhang},
journal= {arXiv preprint arXiv:2503.19052},
year = {2025}
}