Mean curvature flow solitons from symmetry group viewpoint

TL;DR

This paper investigates the symmetry groups of the mean curvature flow in Riemannian manifolds, introduces generalized solitons, and classifies affine solutions as self-similar, expanding understanding of flow symmetries and soliton structures.

Contribution

It characterizes the symmetry group of the mean curvature flow and defines generalized solitons, including examples in non-Euclidean surfaces and a classification of affine solutions.

Findings

Symmetry group of mean curvature flow determined

Generalized solitons defined and exemplified

All affine solutions are self-similar

Abstract

The symmetry group of the mean curvature flow in general ambient Riemannian manifolds is determined, based on which we define generalized solitons to the mean curvature flow. We also provide examples of homothetic solitons in non-Euclidean surfaces and prove that all the affine solutions to the mean curvature flow are self-similar solutions.