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<p>We establish three-circle theorems for subharmonic functions on Riemannian manifolds with nonnegative Ricci curvature, as well as on shrinking gradient Ricci solitons with scalar curvature bounded from below by <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11425_2024_2332_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({n-2}\over{2}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mfrac> <mrow> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </math></EquationSource> </InlineEquation>. We also establish a three-circle theorem for holomorphic functions on shrinking gradient Kähler-Ricci solitons with some curvature conditions. As applications, we prove some Liouville-type theorems.</p>

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Three-circle theorems and Liouville-type theorems

  • 期刊论文

  • 发表日期：

    2025年1月21日

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  • Run-Qiang Jian,
  • Zhuhong Zhang

摘要

We establish three-circle theorems for subharmonic functions on Riemannian manifolds with nonnegative Ricci curvature, as well as on shrinking gradient Ricci solitons with scalar curvature bounded from below by \({n-2}\over{2}\) n − 2 2 . We also establish a three-circle theorem for holomorphic functions on shrinking gradient Kähler-Ricci solitons with some curvature conditions. As applications, we prove some Liouville-type theorems.