Sharp Concavity of the Isoperimetric Profile Under Lower Ricci Bounds - Workshop on Synthetic Curvature Bounds

Explore a 53-minute conference talk from the Workshop on "Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension" held at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the generalization of the sharp concavity inequality for isoperimetric profiles in RCD (K,N) spaces, extending beyond the work of Bavard-Pansu on smooth Riemannian manifolds. Examine the relationship between lower Ricci curvature bounds and isoperimetric profile concavity, and investigate open questions that arise when Riemannian or finite dimensionality assumptions are removed. Gain insights into the collaborative research conducted by Semola, Antonelli, Pasqualetto, and Pozzetta in this advanced mathematical exploration.