Liouville theorem for $V$-harmonic heat flows

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.

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