Volume-preserving mean curvature flow for tubes in symmetric spaces

TL;DR

This paper studies the evolution of tubes in symmetric spaces under volume-preserving mean curvature flow, showing that the tubular structure remains intact under specific conditions.

Contribution

It introduces conditions under which the volume-preserving mean curvature flow preserves the tubular shape in symmetric spaces.

Findings

Tubeness is preserved along the flow under certain conditions.

The flow maintains the tube structure over time.

Conditions for preservation depend on the geometry of the initial tube.

Abstract

In this paper, we investigate the volume-prserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space. We prove that the tubeness is preserved along the flow under certain conditions.