https://neckpinch.com/authors/keisuke-takasao/New arXiv papers by Keisuke Takasao, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.21545arxiv:2610.21545Thu, 15 Oct 2026 00:00:00 GMTFabius Krämer, Tim Laux, Keisuke Takasao — We prove the generic existence of mean curvature flows in spaces with rough weights. Our weak solutions are both unit-density Brakke flows and distributional solutions. Such a generic statement is optimal in the sense that we consider weights that are too rough to have well-defined traces on every hypersurface.Mean curvature flowWeak & singular flows https://arxiv.org/abs/2608.26842arxiv:2608.26842Thu, 27 Aug 2026 00:00:00 GMTTim Laux, Keisuke Takasao — Since Ilmanen's pioneering work [J. Differential Geom. 38, 417-461, (1993)] it has been a major open problem to understand the sharp-interface limit of systems of coupled Allen-Cahn equations. We prove - for the first time - a global, unconditional convergence result for such a coupled system and show that the limit is a multiphase mean curvature flow in the sense of Brakke.Mean curvature flowWeak & singular flowsPhase fields & multiphase flows https://arxiv.org/abs/2507.06150arxiv:2507.06150Tue, 08 Jul 2025 00:00:00 GMTTim Laux, Keisuke Takasao — We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalizes the violation of the constraint, and pass to the limit. The resulting level set formulation has unique solutions - up to fattening. Extending the work of Evans and Spruck and a work by Ullrich and one of the authors, we show that generic level sets of this flow are distributional solutions of the obstacle problem.Mean curvature flowWeak & singular flows https://arxiv.org/abs/2505.23222arxiv:2505.23222Thu, 29 May 2025 00:00:00 GMTAndrea Chiesa, Keisuke Takasao — In this paper, we propose a new notion of Brakke inequality for volume preserving mean curvature flow. We show the existence of integral varifolds solving the flow globally-in-time in the corresponding Brakke sense using the phase field method. Moreover, such varifolds are solutions to volume preserving mean curvature flow in the L²-flow sense as well. We thus extend a previous result by one of the authors [25].Mean curvature flowVolume-preserving & constrained flowsWeak & singular flowsPhase fields & multiphase flows https://arxiv.org/abs/2201.10850arxiv:2201.10850Wed, 26 Jan 2022 00:00:00 GMTKeisuke Takasao — In this paper, we construct a family of integral varifolds, which is a global weak solution to the volume preserving mean curvature flow in the sense of L²-flow. This flow is also a distributional BV-solution for a short time, when the perimeter of the initial data is sufficiently close to that of ball with the same volume. To construct the flow, we use the Allen–Cahn equation with non-local term motivated by studies of Mugnai, Seis, and Spadaro, and Kim and Kwon. We prove the convergence of the solution for the Allen–Cahn equation to the family of integral varifolds with only natural assumptions for the initial data.Mean curvature flowVolume-preserving & constrained flowsWeak & singular flowsPhase fields & multiphase flows https://arxiv.org/abs/2112.11069arxiv:2112.11069Tue, 21 Dec 2021 00:00:00 GMTTakashi Kagaya, Masashi Mizuno, Keisuke Takasao — The mathematical model of grain boundary motion, including lattice misorientations' effect, is considered. When time-dependent lattice misorientations are state variables of the surface tension of the grain boundary, to ensure the energy dissipation law, one can obtain a curvature flow of networks with time-dependent mobilities. This paper studies the solvability and long-time asymptotic behavior of the curvature flow subjected to the Herring condition which ensures that the constituent grain boundary surface tensions are balanced at the triple junction.Other curvature flowsLong-time existence & convergencePhase fields & multiphase flows