Mean curvature flow of singular Riemannian foliations

2014/08/22 by Marcos M. Alexandrino, Marco Radeschi, Alexandrino, Marcos +1 · 1 citation
Mathematics · #53C12 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1408.5433

openalex publication_date 2014/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a singular Riemannian foliation on a compact Riemannian manifold, we study the mean curvature flow equation with a regular leaf as initial datum. We prove that if the leaves are compact and the mean curvature vector field is basic, then any finite time singularity is a singular leaf, and the singularity is of type I. These results generalize previous results of Liu and Terng, Pacini and Koike. In particular our results can be applied to partitions of Riemannian manifolds into orbits of actions of compact groups of isometries.

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• Manifold submetries from compact homogeneous spaces

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