Boundary regularity and stability under lower Ricci bounds

Régularité et stabilité des frontières sous les bornes inférieures de Ricci

Daniele Semola (1) , Fanny Bastien (2) , Hugo Béchet (2)

1 Mathematical Institute, University of Oxford
2 IF - Institut Fourier

Summer school 2021. The theory of non smooth spaces with lower Ricci Curvature bounds has undergone huge developments in the last thirty years. On the one hand the impetus came from Gromov’s precompactness theorem and the Cheeger-Colding theory of Ricci limit spaces. On the other hand “synthetic” theories of lower Ricci bounds have been developed, based on semigroup tools (the Bakry-Émery theory) and on Optimal Transport (the Lott-Sturm-Villani theory). The Cheeger-Colding theory did not consider manifolds with boundary, while in the synthetic framework even understanding what is a good definition of boundary is a challenge. The aim of this talk is to present some recent results obtained in collaboration with E. Bruè (IAS, Princeton) and A. Naber (Northwestern University) about regularity and stability for boundaries of spaces with lower Ricci Curvature bounds.

Mots clés: lower Ricci bounds; curvature constraints and spaces of metrics; grenoble; eem2021; lower Ricci bounds

Mots clés: contraintes de courbures et espaces métriques; contraintes de courbures et espaces métriques

Domaines: Mathématiques [math]

Daniele Semola, Fanny Bastien, Hugo Béchet. Boundary regularity and stability under lower Ricci bounds: Curvature Constraints and Spaces of Metrics. 2021. ⟨hal-03677366⟩