On mean curvature flow of singular Riemannian foliations: Noncompact cases

Autor(es)

Alexandrino, Marcos M. ; Cavenaghi, Leonardo F. ; Goncalves, Icaro

• Tipo de documento: Artigo Científico
• Fonte: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 72, p. 18-pg., 2020-10-01.

Resumo

In this paper we investigate the mean curvature flow (MCF) of a regular leaf of a closed generalized isoparametric foliation as initial datum, generalizing previous results of Radeschi and the first author. We show that, under bounded curvature conditions, any finite time singularity is a singular leaf, and the singularity is of type I. The new techniques also allow us to discuss the existence of basins of attraction, how cylinder structures can affect convergence of basic MCF of immersed submanifolds and assure convergence of MCF of non-closed leaves of generalized isoparametric foliation on compact manifold. (C) 2020 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 17/24680-1 - Deformações métricas e aplicações
• Beneficiário: Leonardo Francisco Cavenaghi
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 16/23746-6 - Técnicas algébricas, topológicas e analíticas em geometria diferencial e análise geométrica
• Beneficiário: Paolo Piccione
• Modalidade de apoio: Auxílio à Pesquisa - Temático