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<p>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 <i>V</i>-harmonic map heat flows. Furthermore, we can also derive a Liouville theorem for quasi-harmonic maps under an exponential growth condition.</p>

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Liouville Theorems for Ancient Solutions to the V-harmonic Map Heat Flows II

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Qun Chen,
  • Hongbing Qiu

摘要

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.