Liouville theorem for $V$-harmonic heat flows

TL;DR

This paper studies $V$-harmonic heat flows between certain Riemannian manifolds, providing gradient estimates for ancient solutions and establishing a Liouville theorem, advancing understanding of geometric heat flow behavior.

Contribution

It introduces a Liouville theorem for $V$-harmonic heat flows and derives gradient estimates for ancient solutions under curvature conditions.

Findings

Gradient estimates for ancient solutions

Liouville theorem for $V$-harmonic heat flows

Results under nonnegative Bakry-Emery Ricci curvature

Abstract

In this paper, we investigate $V$-harmonic heat flows from complete Riemannian manifolds with nonnegative Bakry-Emery Ricci curvature to complete Riemannian manifolds with sectional curvature bounded above. We give a gradient estimate of ancient solutions to this flow and establish a Liouville type theorem.