https://neckpinch.com/authors/hiroyoshi-mitake/New arXiv papers by Hiroyoshi Mitake, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2401.05156arxiv:2401.05156Wed, 10 Jan 2024 00:00:00 GMTHiroyoshi Mitake, Yusuke Oka, Hung Vinh Tran — Here, we study the motion of axisymmetric hypersurfaces \Γₜ\_(t≥0) evolved by forced mean curvature flows in the periodic setting. We establish conditions that quenching occurs or does not occur in terms of the initial data and forcing term. We also study the locations where the quenching happens in some special cases.Mean curvature flowVolume-preserving & constrained flows https://arxiv.org/abs/2312.08362arxiv:2312.08362Wed, 13 Dec 2023 00:00:00 GMTHiroyoshi Mitake, Hung V. Tran — Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appropriate conditions on the forcing term, we prove that the solution is globally Lipschitz. We then study the large time average of the solution and deduce the asymptotic growth rate of the crystal. Some large time behavior results of the solution are obtained.Mean curvature flowVolume-preserving & constrained flowsHomogeneous spacesBoundaries & non-compactFree boundary & capillary https://arxiv.org/abs/2306.14218arxiv: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 https://arxiv.org/abs/2108.01244arxiv:2108.01244Tue, 03 Aug 2021 00:00:00 GMTJiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake, Hung Vinh Tran — Here, we study a level-set forced mean curvature flow with the homogeneous Neumann boundary condition. We first show that the solution is Lipschitz in time and locally Lipschitz in space. Then, under an additional condition on the forcing term, we prove that the solution is globally Lipschitz. We obtain the large time behavior of the solution in this setting and study the large time profile in some specific situations. Finally, we give two examples demonstrating that the additional condition on the forcing term is sharp, and without it, the solution might not be globally Lipschitz.Mean curvature flowVolume-preserving & constrained flowsHomogeneous spacesBoundaries & non-compactFree boundary & capillary