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

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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.

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