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arXiv · 2412.04684

Liouville theorems for ancient solutions to the V-harmonic map heat flows II

Qun Chen·Hongbing Qiu
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Abstract

When the domain is a complete noncompact Riemannian manifold with nonnegative Bakry--Emery Ricci curvature and the target is a complete Riemannian manifold with sectional curvature bounded above by a positive constant, by carrying out refined gradient estimates, we obtain a better Liouville theorem for ancient solutions to the V-harmonic map heat flows. Furthermore, we can also derive a Liouville theorem for quasi-harmonic maps under an exponential growth condition.

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Qun Chen, Hongbing Qiu. 2024-12-06. Liouville theorems for ancient solutions to the V-harmonic map heat flows II. https://arxiv.org/abs/2412.04684

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