https://neckpinch.com/authors/takashi-kagaya/New arXiv papers by Takashi Kagaya, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2510.04566/arxiv:2510.04566Mon, 06 Oct 2025 00:00:00 GMTTakashi Kagaya, Masatomo Takahashi — In this paper, we deal with an inverse curvature flow of ℓ-convex Legendre curves. Since the Legendre curve is a natural generalization of regular curve, the flow is a generalization of the classical inverse curvature flow of regular curves. For the initial value problem, we study on the unique existence of the flow in global time, the monotonicity of the number of the singular cusps with respect to t > 0 and the asymptotic behavior of the flow as t → ∞. Regarding the asymptotics, the flow asymptotically converges to one of the self similar solutions by scaling appropriately, and the convergence is completely categorized depending on the initial curve.Other curvature flowsInverse mean curvature flow https://neckpinch.com/papers/2112.11069/arxiv: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