Collapse of the Mean Curvature Flow for Equifocal Submanifolds

Abstract

In this paper, we investigate the mean curvature flows having an equifocal submanifold in a symmetric space of compact type and its focal submanifolds as initial data. It is known that an equifocal submanifold of codimension greater than one in an irreducible symmetric space of compact type occurs as a principal orbit of a Hermann action. However, we investigate the flows conceptionally without use of this fact. The investigation is performed by investigating the mean curvature flows having the lifts of the submanifolds to an (infinite dimensional separable) Hilbert space through a Riemannian submersion as initial data.