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Stability of eigenvalues and observable diameter in RCD$(1,infty)$ spaces

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 نشر من قبل Jerome Bertrand
 تاريخ النشر 2021
  مجال البحث
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We study stability of the spectral gap and observable diameter for metricmeasure spaces satisfying the RCD(1, $infty$) condition. We show that if such a space has an almost maximal spectral gap, then it almost contains a Gaussian component, and the Laplacian has eigenvalues that are close to any integers, with dimension-free quantitative bounds. Under the additional assumption that the space admits a needle disintegration, we show that the spectral gap is almost maximal iff the observable diameter is almost maximal, again with quantitative dimension-free bounds.



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