Existence of weak mean curvature flow with prescribed contact angle via elliptic regularization

Autor:	Tashiro, Kiichi
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs 53E10 (primary) 28A75 35K75
Druh dokumentu:	Working Paper
Popis:	In the present paper, we study the existence of Brakke-type weak mean curvature flow satisfying the contact angle condition for general angle $ \theta \in ( 0 , \pi ) $ 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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.12283 Zobrazit plný text záznamu View this record from Arxiv