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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((M, g(s))_{s\in [0,\infty )}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>g</mi> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>s</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo stretchy="false">)</mo> </mrow> </msub> </math></EquationSource> </InlineEquation> be an admissible, complete backward <i>K</i>-super Ricci flow, and let <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((N, \mathfrak {h})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo>,</mo> <mi mathvariant="fraktur">h</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be a simply connected, complete Riemannian manifold with nonpositive sectional curvature. We establish Liouville theorems for solutions to the heat flow of backward quasi-harmonic maps along ancient <i>K</i>-super Ricci flow, adopting Perelman’s reduced geometric viewpoint. These results extend and generalize the related results of Li-Wang [J. Eur. Math. Soc. 11(1), (2009) 207-221], and Kunikawa-Sakurai [Calc. Var. 60, (2021) 199].</p>

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Liouville theorems for heat flow of quasi-harmonic maps along ancient K-super Ricci flow via reduced geometry

  • 期刊论文

  • 发表日期：

    2026年3月11日

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  • Wen Wang

摘要

Let \((M, g(s))_{s\in [0,\infty )}\) ( M , g ( s ) ) s ∈ [ 0 , ∞ ) be an admissible, complete backward K-super Ricci flow, and let \((N, \mathfrak {h})\) ( N , h ) be a simply connected, complete Riemannian manifold with nonpositive sectional curvature. We establish Liouville theorems for solutions to the heat flow of backward quasi-harmonic maps along ancient K-super Ricci flow, adopting Perelman’s reduced geometric viewpoint. These results extend and generalize the related results of Li-Wang [J. Eur. Math. Soc. 11(1), (2009) 207-221], and Kunikawa-Sakurai [Calc. Var. 60, (2021) 199].