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Videos Year : 2021

D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato condition

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Fanny Bastien
Hugo Béchet
  • Function : Producer

Abstract

I will present a joint work with G. Carron and I. Mondello where we study Kato limit spaces. These are metric measure spaces obtained as Gromov-Hausdorff limits of smooth n-dimensional Riemannian manifolds with Ricci curvature satisfying a uniform Kato-type condition. In this context, strictly wider than the ones of Ricci limit spaces (where the Ricci curvature satisfies a uniform lower bound) and Lp-Ricci limit spaces (where the Ricci curvature is uniformly bounded in Lp for some p>n/2), we extend classical results of Cheeger, Colding and Naber, like the fact that under a non-collapsing assumption, every tangent cone is a metric measure cone. I will present these results and explain how we rely upon a new heat-kernel based almost monotone quantity to derive them.

Dates and versions

hal-03329606 , version 1 (31-08-2021)

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Attribution - NonCommercial - NoDerivatives

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  • HAL Id : hal-03329606 , version 1

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David Tewodrose, Fanny Bastien, Hugo Béchet. D. Tewodrose - Limits of Riemannian manifolds satisfying a uniform Kato condition: Summer School 2021 - Curvature Constraints and Spaces of Metrics. 2021. ⟨hal-03329606⟩
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