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

Differential Geometry 2024-12-09 v1

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.

Keywords

Cite

@article{arxiv.2412.04684,
  title  = {Liouville theorems for ancient solutions to the V-harmonic map heat flows II},
  author = {Qun Chen and Hongbing Qiu},
  journal= {arXiv preprint arXiv:2412.04684},
  year   = {2024}
}

Comments

This version had been submitted to a math journal in this May