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<p>In this paper, we prove a pseudolocality-type theorem for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal L\)</EquationSource> </InlineEquation>-complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In particular, we prove the strong uniqueness theorem for the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal L\)</EquationSource> </InlineEquation>-complete Ricci flow on the Euclidean space. This partially answers a question proposed by B-L.&#xa0;Chen (J Differ Geom 82(2):363–382, 2009).</p>

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Pseudolocality and Uniqueness of Ricci Flow on Almost Euclidean Noncompact Manifolds

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • Liang Cheng,
  • Yongjia Zhang

摘要

In this paper, we prove a pseudolocality-type theorem for \(\mathcal L\) -complete noncompact Ricci flow which may not have bounded sectional curvature; with the help of it we study the uniqueness of the Ricci flow on noncompact manifolds. In particular, we prove the strong uniqueness theorem for the \(\mathcal L\) -complete Ricci flow on the Euclidean space. This partially answers a question proposed by B-L. Chen (J Differ Geom 82(2):363–382, 2009).