https://neckpinch.com/authors/hiuri-fellipe-santos-dos-reis/New arXiv papers by Hiuri Fellipe Santos dos Reis, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2005.10688/arxiv:2005.10688Thu, 21 May 2020 00:00:00 GMTBenedito Leandro, Rafael Novais, Hiuri F. S. dos Reis — In this paper we make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in ℝ³. We prove that self-similar solutions of the MCF by non-cylindrival surfaces and conical surfaces in ℝ³ are trivial. Moreover, we characterize the self-similar solutions of the MCF by surfaces of revolutions under a homothetic helicoidal motion in ℝ³ in terms of the curvature of the generating curve. Finally, we characterize the self-similar solutions for the MCF by cylindrical surfaces under a homothetic helicoidal motion in ℝ³. Explicit families of exact solutions for the MCF by cylindrical surfaces in ℝ³ are also given.Mean curvature flowRotational symmetry & warped products https://neckpinch.com/papers/1904.12015/arxiv:1904.12015Fri, 26 Apr 2019 00:00:00 GMTBenedito Leandro, Adriana Araujo Cintra, Hiuri Fellipe dos Santos Reis — The aim of this paper is to investigate the mean curvature flow soliton solutions on the Heisenberg group 𝓗 when the initial data is a ruled surface by straight lines. We give a family of those solutions which are generated by Iso₀(𝓗) (the isometries of 𝓗 for which the origin is a fix point). We conclude that the function which describe the motion of these surfaces under MCF, is always a linear affine function. As an application we proof that the Grim Reaper solution evolves from a ruled surface in 𝓗. We also provide other examples.Mean curvature flowSelf-shrinkers & translators https://neckpinch.com/papers/1710.02122/arxiv:1710.02122Thu, 05 Oct 2017 00:00:00 GMTHiuri Fellipe Santos dos Reis, Keti Tenenblat — It is shown that a hypersurface of a space form is the initial data for a solution to the mean curvature flow by parallel hypersurfaces if, and only if, it is isoparametric. By solving an ordinary differential equation, explicit solutions are given for all isoparametric hypersurfaces of space forms. In particular, for such hypersurfaces of the sphere, the exact collapsing time into a focal submanifold is given in terms of its dimension, the principal curvatures and their multiplicities.Mean curvature flow(Non)collapsingSphere theorems