Positive curvatures, exotic manifolds and Riemannian foliations
Geometry and topology of Riemannian foliations via deformations
| Full text | |
| Author(s): |
Alexandrino, Marcos M.
;
Cavenaghi, Leonardo F.
;
Goncalves, Icaro
Total Authors: 3
|
| Document type: | Journal article |
| Source: | DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 72, p. 18-pg., 2020-10-01. |
| Abstract | |
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) | |
| FAPESP's process: | 17/24680-1 - Metric deformations and applications |
| Grantee: | Leonardo Francisco Cavenaghi |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 16/23746-6 - Algebraic, topological and analytical techniques in differential geometry and geometric analysis |
| Grantee: | Paolo Piccione |
| Support Opportunities: | Research Projects - Thematic Grants |