通过椭圆正则化实现带预定接触角的弱均曲率流
微分几何
2024-12-09 v3 偏微分方程分析
摘要
本文研究了通过 Ilmanen 正则化方法，构建满足接触角条件的 Brakke 类型弱均曲率流的存在性，该接触角范围为一般角度 。本文的主要技术包括：建立具有接触角条件的 varifold 的紧性定理，并将 Ilmanen 的正则化方法推广到毛细作用中。
引用
@article{arxiv.2410.12283,
title = {Existence of weak mean curvature flow with prescribed contact angle via elliptic regularization},
author = {Kiichi Tashiro},
journal= {arXiv preprint arXiv:2410.12283},
year = {2024}
}
备注
The paper consists of 28 pages and includes 2 figures. I have corrected the mistakes from the first draft and revised many explanations: We impose assumptions that the first variations are uniformly bounded to prove the compactness theorems. Additionally, we have added a new subsection to estimate the first variations of the construction derived from the elliptic regularization