The mean curvature flow for equifocal submanifolds

TL;DR

This paper studies the evolution of equifocal submanifolds under mean curvature flow by lifting them to a Hilbert space via Riemannian submersion, providing insights into their geometric behavior.

Contribution

It introduces a novel approach of analyzing mean curvature flow for equifocal submanifolds through their liftings to Hilbert spaces, expanding understanding of their geometric properties.

Findings

Analysis of mean curvature flow for equifocal submanifolds

Use of Hilbert space lifting via Riemannian submersion

Insights into geometric evolution of these submanifolds

Abstract

In this paper, we investigate the mean curvature flow having equifocal submanifolds as initial data. The investigation are performed by investigating the mean curvature flow having the lifted submanifolds to a Hilbert space through a Riemannian submersion as initial data.