Existence of weak mean curvature flow with prescribed contact angle via elliptic regularization
Differential Geometry
2024-12-09 v3 Analysis of PDEs
Abstract
In the present paper, we study the existence of Brakke-type weak mean curvature flow satisfying the contact angle condition for general angle via Ilmanen's regularization. The main ingredients of the result are the establishment of a compactness theorem for varifolds with the contact angle and the extension of Ilmanen's regularization to the capillarity.
Cite
@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}
}
Comments
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