https://neckpinch.com/authors/zhenghuan-gao/New arXiv papers by Zhenghuan Gao, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2210.16475/arxiv:2210.16475Sat, 29 Oct 2022 00:00:00 GMTZhenghuan Gao, Bendong Lou, Jinju Xu — In this paper we consider a mean curvature flow V=H+A in a high dimensional cylinder Ω× R, where, A is a constant, Ω is a bounded domain in Rⁿ, and, for a hypersurface y=u(x,t) over Ω, V and H denote its normal velocity and mean curvature, respectively. Assume the hypersurface contacts the cylinder boundary ∂Ω× R with prescribed angle θ(x). Under certain assumptions such as Ω is strictly convex and \|cosθ\|_(C²) is small, or Ω is not necessarily convex but |A| is sufficiently large, we derive some {\it uniform-in-time gradient bounds} for the solutions to initial boundary value problems. Then, we present a trichotomy result as well as its criterion for the asymptotic behavior of the solutions, that is, when I:= A|Ω|+∫_∂Ω cosθ(x) dσ>0 (resp. =0, <0), the solution u converges as t→ ∞ to a translating solution with positive speed (resp. stationary solution, a translating solution with negative speed).Mean curvature flowSelf-shrinkers & translatorsFree boundary & capillary