https://neckpinch.com/authors/can-cui/New arXiv papers by Can Cui, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2510.22146/arxiv:2510.22146Sat, 25 Oct 2025 00:00:00 GMTCan Cui, Nung Kwan Yip — Over a bounded strictly convex domain in ℝⁿ with smooth boundary, we establish a priori gradient estimate for an anisotropic mean curvature flow with prescribed contact angle and Neumann boundary conditions. The estimates require careful analysis of the degeneracy property of the anisotropic mean curvature operator. As a result, for both problems, we can infer that the solutions converge to one that is translation invariant in time.Mean curvature flowAnisotropic & nonlocal flowsBoundaries & non-compactFree boundary & capillary https://neckpinch.com/papers/2510.22136/arxiv:2510.22136Sat, 25 Oct 2025 00:00:00 GMTCan Cui, Nung Kwan Yip — In this paper, we study surfaces which evolve by anisotropic mean curvature flow with contact angle boundary condition over a strictly convex domain in ℝ². We establish a prior gradient estimate for smooth solutions to this boundary value problem. The same approach can also handle Dirichlet boundary condition in ℝⁿ, n≥ 2. For both problems, we prove that the solutions converge to one that is translation invariant in time.Mean curvature flowAnisotropic & nonlocal flowsSurfacesBoundaries & non-compactFree boundary & capillary