Non-parametric mean curvature flow with prescribed contact angle in Riemannian products

Abstract

Assuming that there exists a translating soliton $u_{\infty }$ with speed $C$ in a domain $\Omega$ and with prescribed contact angle on $\partial \Omega$, we prove that a graphical solution to the mean curvature flow with the same prescribed contact angle converges to $u_{\infty }+Ct$ as $t\to \infty$. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of $\Omega$ and Ricci curvature in $\Omega$.

This replaces the previous versions. We have added Remark 1.2, Theorem 1.3 and its proof in Section 3

References in corpus (1)

• Translating solitons over Cartan-Hadamard manifolds