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

David Tewodrose (1) , Fanny Bastien (2) , Hugo Béchet (2)

1 ULB - Département de Mathématique [Bruxelles]
2 IF - Institut Fourier

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.

Mots clés: eem2021; curvature constraints and spaces of metrics; Grenoble; Riemannian manifolds; Kato condition

Mots clés: contraintes de courbures et espaces métriques

Domaines: Mathématiques [math]

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⟩