https://neckpinch.com/authors/keti-tenenblat/New arXiv papers by Keti Tenenblat, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2403.14782/arxiv:2403.14782Thu, 21 Mar 2024 00:00:00 GMTAlancoc dos Santos Alencar, Keti Tenenblat — We consider the inverse mean curvature flow by parallel hypersurfaces in space forms. We show that such a flow exists if and only if the initial hypersurface is isoparametric. The flow is characterized by an algebraic equation satisfied by the distance function of the parallel hypersurfaces. The solutions to the flow are obtained explicitly when the distinct principal curvatures have the same multiplicity. This is an additional assumption only for isoparametric hypersurfaces of the hyperbolic space or of the sphere with two or four distinct principal curvatures. The boundaries of the maximal interval of definition, when finite, are determined in terms of the number g of distinct principal curvatures, their multiplicities m and the mean curvature H of the initial hypersurface. We describe the collapsing submanifolds of the flow at the boundaries of the interval. In particular, we show in the Euclidean space the solutions are eternal, while in the hyperbolic space there are eternal and immortal solutions. Starting with a connected isoparametric submanifold of the sphere, we show that the flow is an ancient solution, that collapses into a minimal hypersurface whose square length of its second fundamental form and its scalar curvature are constants given in terms of g and n. The minimal hypersurface is totally geodesic when g=1, it is a Clifford minimal hypersurface of the sphere when g=2 and it is a Cartan type minimal submanifold when g∈\3,4,6\.Mean curvature flowOther curvature flowsInverse mean curvature flowAncient solutions(Non)collapsingSphere theoremsScalar curvatureLong-time existence & convergenceMinimal & CMC surfaces https://neckpinch.com/papers/2109.03677/arxiv:2109.03677Wed, 08 Sep 2021 00:00:00 GMTFabio Nunes da Silva, Keti Tenenblat — We show that the solutions to the curvature flow (CF) for curves on the 2-dimensional light cone are in correspondence with the solutions to the inverse curvature flow (ICF). We prove that the ellipses and the hyperboles are the only curves that evolve under homotheties. The ellipses are the only closed ones and they are ancient solutions. We show that a spacelike curve on the cone is a self-similar solution to the CF (resp. (ICF)) if, only if, its curvature (resp. inverse of its curvature) differs by a constant c from being the inner product between its tangent vector field and a fixed vector v of the 3-dimensional Minkowski space. The curve is a soliton solution when c=0. We prove that, for each vector v there exists a 2-parameter family of self-similar solutions to the CF and to the ICF, on the light cone. Moreover, at each end of such a curve, the curvature is either unbounded or it tends to 0 or to the constant c. Explicitly given soliton solutions are included and some self-similar solutions on the light cone, are visualized.Other curvature flowsInverse mean curvature flowAncient solutions3-manifoldsSurfacesPhysicsNumerics & visualization