Mean curvature flow solitons in the presence of conformal vector fields

TL;DR

This paper introduces a generalized concept of mean curvature flow solitons applicable to various target spaces, including constant curvature, Riemannian products, and warped products, broadening the scope of geometric flow analysis.

Contribution

The paper defines a new, more inclusive notion of mean curvature flow solitons suitable for diverse geometric settings.

Findings

Unified framework for mean curvature flow solitons in different ambient spaces

Extension of soliton theory to warped product spaces

Potential applications in geometric analysis and topology

Abstract

The aim of this paper is to introduce a notion of mean curvature flow soliton general enough to encompass target spaces of constant sectional curvature, Riemannian products or, in increasing generality, warped product spaces.