Translating surfaces of the non-parametric mean curvature flow with prescribed contact angle
The authors study the mean curvature flow of two dimensional graphs over convex domains in \(\mathbb{R}^ 2\) with prescribed contact angle at the boundary. Under some reasonable assumptions they show that such a graph remains smooth and converges as \(t\to\infty\) to a unique graph moving by translation at constant speed. This generalizes an earlier work of the authors [Math. Ann. 295, No. 4, 761-765 (1993; Zbl 0798.35063)] on the one dimensional case, and of \textit{G. Huisken} [J. Differ. Equations 77, No. 2, 369-378 (1989; Zbl 0686.34013)], who proved an analogous result in any dimension for the special case of vertical contact angle.
scientific article; zbMATH DE number 509955