https://neckpinch.com/authors/hengyu-zhou/New arXiv papers by Hengyu Zhou, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2506.23245/arxiv:2506.23245Sun, 29 Jun 2025 00:00:00 GMTCaiyan Li, Hengyu Zhou — In this paper, we propose a new assumption (1.2) that involves a small oscillation and C² norms for maps from smooth bounded domains into Euclidean spaces. Furthermore, by assuming that the domain has non-negative Ricci curvature, we establish the Dirichlet problem for the minimal surface system via the mean curvature flow (MCF) with boundary. The long-time existence of such flow is derived using Bernstein-type theorems of higher codimensional self-shrinkers in the whole space and the half-space. Another novel aspect is that our hypothesis imposes no restriction on the diameter of the domains, which implies an existence result for an exterior Dirichlet problem of the minimal surface system.Mean curvature flowSelf-shrinkers & translatorsLong-time existence & convergenceMinimal & CMC surfaces