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

2024/10/16 by Tashiro, Kiichi
#28A75 #35K75 #53E10 (primary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.12283

Abstract

In the present paper, we study the existence of Brakke-type weak mean curvature flow satisfying the contact angle condition for general angle θ∈ ( 0 , π) 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.

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