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<p>In this paper we classify rotationally symmetric locally conformally flat admissible solitons to the <i>k</i>-Yamabe flow, a fully non-linear version of the Yamabe flow. For <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2044_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\ge 2k\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>2</mn> <mi>k</mi> </mrow> </math></EquationSource> </InlineEquation> we prove existence of complete expanding, steady and shrinking solitons and describe their asymptotic behavior at infinity. For <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2044_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(n&lt;2k\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>&lt;</mo> <mn>2</mn> <mi>k</mi> </mrow> </math></EquationSource> </InlineEquation> we prove that steady and expanding solitons are not admissible. The proof is based on the careful analysis of an associated dynamical system.</p>

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On the Existence and Classification of k-Yamabe Gradient Solitons

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Maria Fernanda Espinal,
  • Mariel Sáez

摘要

In this paper we classify rotationally symmetric locally conformally flat admissible solitons to the k-Yamabe flow, a fully non-linear version of the Yamabe flow. For \(n\ge 2k\) n ≥ 2 k we prove existence of complete expanding, steady and shrinking solitons and describe their asymptotic behavior at infinity. For \(n<2k\) n < 2 k we prove that steady and expanding solitons are not admissible. The proof is based on the careful analysis of an associated dynamical system.