https://neckpinch.com/authors/tomoki-fujii/New arXiv papers by Tomoki Fujii, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2308.15790arxiv:2308.15790Wed, 30 Aug 2023 00:00:00 GMTTomoki Fujii, Naoyuki Koike — In this paper, we consider translators (for the mean curvature flow) given by a graph of a function on a symmetric space G/K of compact type which is invariant under a hyperpolar action on G/K. First, in the case of G/K=SO(n+1)/SO(n), SU(n+1)/S(U(1)× U(n)), Sp(n+1)/(Sp(1)× Sp(n)) or F₄/rm Spin(9), we classify the shapes of translators in G/K×ℝ given by the graphs of functions on G/K which are invariant under the isotropy action Kcurvearrowright G/K. Next, in the case where G/K is of higher rank, we investigate translators in G/K×ℝ given by the graphs of functions on G/K which are invariant under a hyperpolar action Hcurvearrowright G/K of cohomogeneity two.Mean curvature flowSelf-shrinkers & translatorsHomogeneous spaces https://arxiv.org/abs/2207.03653arxiv:2207.03653Fri, 08 Jul 2022 00:00:00 GMTTomoki Fujii — In this paper, we consider a translating soliton for the inverse mean curvature flow given as a graph of a function on a domain in a unit sphere whose level sets give isoparametric foliation. First, we show that such function is given as a composition of an isoparametric function on the unit sphere and a function which is given as a solution of a certain ordinary differential equation. Further, we analyze the shape of the graphs of the solutions of the ordinary differential equation. This analysis leads to the classification of the shape of such translating solitons for the inverse mean curvature flow.Mean curvature flowOther curvature flowsInverse mean curvature flowSelf-shrinkers & translators https://arxiv.org/abs/2109.14809arxiv:2109.14809Thu, 30 Sep 2021 00:00:00 GMTTomoki Fujii — In this paper, we consider a translating soliton for the mean curvature flow starting from a graph of a function on a domain in a unit sphere which is constant along each leaf of isoparametric foliation. First, we show that such a function is given as a composition of an isoparametric function on the sphere and a function which is given as a solution of a certain ordinary differential equation. Further, we analyze the shape of the graphs of the solutions of the ordinary differential equation. This analysis leads to the classification of the shape of such translating solitons. Finally, we investigate a domain of the function which is given as a composition of the isoparametric function and the solution of the ordinary differential equation in the case where the number of distinct principal curvatures of the isoparametric hypersurface defined by the regular level set for the isoparametric function is 1, 2, or 3.Mean curvature flowSelf-shrinkers & translators