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<p>We give a new proof of the Smale conjecture for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="222_2025_1334_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">RP</mi> <mn>3</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{RP}^{3}$</EquationSource> </InlineEquation> and all lens spaces using minimal surfaces and min-max theory. For <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="222_2025_1334_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">RP</mi> <mn>3</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{RP}^{3}$</EquationSource> </InlineEquation>, the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.</p>

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The Smale conjecture and min-max theory

  • 期刊论文

  • 发表日期：

    2025年4月4日

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  • Daniel Ketover,
  • Yevgeny Liokumovich

摘要

We give a new proof of the Smale conjecture for RP 3 $\mathbb{RP}^{3}$ and all lens spaces using minimal surfaces and min-max theory. For RP 3 $\mathbb{RP}^{3}$ , the conjecture was first proved in 2019 by Bamler-Kleiner using Ricci flow.