A Liouville theorem of VT-harmonic map heat flow

TL;DR

This paper establishes Liouville theorems for VT-harmonic map heat flow, demonstrating conditions under which solutions must be trivial, thereby advancing understanding of geometric flows on evolving and complete manifolds.

Contribution

It introduces Liouville theorems for VT-harmonic map heat flow from both evolution and complete manifolds into generalized regular balls, extending previous results in geometric analysis.

Findings

Liouville theorem for backward VT-harmonic map heat flow from evolution manifolds

Liouville theorem for VT-harmonic map heat flow from complete manifolds

Results apply to maps into generalized regular balls

Abstract

We proved an Liouville theorem for Backward V T-harmonic map heat flow from evolution manifolds into generalized regular ball. Among others, we also proved an Liouville theorem for V T-harmonic map heat flow from complete manifolds into generalized regular ball.