Non-Parametric Mean Curvature Flow with Prescribed Contact Angle in Riemannian Products

Abstract

Assuming that there exists a translating soliton u∞ with speed C in a domain Ω and with prescribed contact angle on ∂Ω, we prove that a graphical solution to the mean curvature ow with the same prescribed contact angle converges to u∞ + Ct as t → ∞. We also generalize the recent existence result of Gao, Ma, Wang and Weng to non-Euclidean settings under suitable bounds on convexity of Ω and Ricci curvature in Ω.