https://neckpinch.com/authors/xingzhi-bian/New arXiv papers by Xingzhi Bian, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2306.14218/arxiv:2306.14218Sun, 25 Jun 2023 00:00:00 GMTXingzhi Bian, Yoshikazu Giga, Hiroyoshi Mitake — We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is globally solvable, our method gives a global-in-time level-set mean curvature flow under a prescribed boundary with no restriction of the profile of an initial hypersurface. We show that our solution agrees with a classical mean curvature flow under the Dirichlet condition. We moreover prove that our solution agrees with a level-set flow under the Dirichlet condition constructed by P. Sternberg and W. P. Ziemer (1994), where the initial hypersurface is contained in a strictly mean-convex domain and the prescribed boundary is on the boundary of the domain.Mean curvature flowWeak & singular flowsHomogeneous spacesLong-time existence & convergence