C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1

Christina Sormani (1, 2) , Fanny Bastien (3) , Hugo Béchet (3)

1 Department of Mathematics [New York CUNY]
2 Lehman College [CUNY]
3 IF - Institut Fourier

We introduce various notions of convergence of Riemannian manifolds and metric spaces. We then survey results and open questions concerning the limits of sequences of Riemannian manifolds with uniform lower bounds on their scalar curvature. We close the course by presenting methods and theorems that may be applied to prove these open questions including older techniques developed with Lakzian, with Huang and Lee, and with Portegies. I will also present key new results of Allen and Perales. Students and postdocs interested in working on these problems will be formed into teams. For a complete list of papers about intrinsic flat convergence see: https://sites.google.com/site/intrinsicflatconvergence/

Mots clés: eem2021; grenoble; curvature constraints and spaces of metrics; intrinsic flat; Gromov-Hausdorff

Mots clés: contraintes de courbures et espaces métriques

Domaines: Mathématiques [math]

Christina Sormani, Fanny Bastien, Hugo Béchet. C. Sormani - Intrinsic Flat and Gromov-Hausdorff Convergence 1: Summer School 2021 - Curvature Constraints and Spaces of Metrics. 2021. ⟨hal-03379618⟩