Nonparametric Mean Curvature Flow with Nearly Vertical Contact Angle Condition

Abstract

For any bounded strictly convex domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary, we find the prescribed contact angle which is nearly perpendicular such that nonparametric mean curvature flow with contact angle boundary condition converge to ones which move by translation. Subsequently, the existence and uniqueness of smooth solutions to the capillary problem without gravity on strictly convex domain are also discussed.