Calculus of Variations and Geometric Measure Theory

Boundary regularity and stability under lower Ricci curvature bounds

Daniele Semola (Fields Institute)

created by pinamonti on 28 May 2021

1 jun 2021 -- 14:30   [open in google calendar]

Zoom seminari

Please write to or to Andrea.marchese@unitn if you want to attend the seminar.


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 from 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.