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<p>In this paper we develop a general ‘analytic’ splitting principle for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2135_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textsf{RCD}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">RCD</mi> </math></EquationSource> </InlineEquation> spaces: we show that if there is a function with suitable Laplacian and Hessian, then the space is (isomorphic to) a warped product. Our result covers most of the splitting-like results currently available in the literature about <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2135_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textsf{RCD}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="sans-serif">RCD</mi> </math></EquationSource> </InlineEquation> spaces. We then apply it to extend to the non-smooth category some structural property of Riemannian manifolds obtained by Li and Wang.</p>

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A General Splitting Principle on \(\textsf{RCD}\) Spaces and Applications to Spaces with Positive Spectrum

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Nicola Gigli,
  • Fabio Marconi

摘要

In this paper we develop a general ‘analytic’ splitting principle for \(\textsf{RCD}\) RCD spaces: we show that if there is a function with suitable Laplacian and Hessian, then the space is (isomorphic to) a warped product. Our result covers most of the splitting-like results currently available in the literature about \(\textsf{RCD}\) RCD spaces. We then apply it to extend to the non-smooth category some structural property of Riemannian manifolds obtained by Li and Wang.