VARIFOLDS WITH CAPILLARY BOUNDARY

作     者：Wang, Guofang Zhang, Xuwen 

作者机构：Mathematisches Institut Universität Freiburg Ernst-Zermelo-Str.1 Freiburg79104 Germany 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2025年

核心收录：

主　　题：Boundary conditions 

摘      要：In this paper we introduce and study a new class of varifolds in Rn+1 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 *** Codes 49Q15, 53C42 Copyright © 2025, The Authors. All rights reserved.