The translating soliton of mean curvature flow

TL;DR

This paper investigates fundamental properties of translating solitons in mean curvature flow, including volume growth, maximum principles, Gauss maps, and curvature estimates, leading to rigidity theorems in higher codimension.

Contribution

It provides new estimates and rigidity results for translating solitons, extending understanding in higher codimension settings.

Findings

Established volume growth and maximum principles for translating solitons.

Derived point-wise and integral estimates for the second fundamental form.

Proved rigidity theorems for translating solitons in higher codimension.

Abstract

We study some basic problems of translating solitons: the volume growth, generalized maximum principle, Gauss maps and certain functions related to the Gauss maps, finally we carry out point-wise estimates and integral estimates for the squared norm of the second fundamental form. Those estimates give rigidity theorems for translating solitons in the Euclidean space in higher codimension.