Sharp concavity of the isoperimetric profile under lower Ricci bounds: recent results and open questions

Daniele Semola (ETH Zurich)

May 24. 2024, 11:10 — 11:55

Starting with the work of Bavard-Pansu in the eighties it was understood that a lower bound on the Ricci curvature of a smooth Riemannian manifold leads to a sharp concavity inequality for its isoperimetric profile. In joint work with Antonelli, Pasqualetto, and Pozzetta we generalized such inequality to the case of $\mathrm{RCD}(K,N)$ spaces, for $N<\infty$. In this talk, I will review the problem and discuss some open questions that are left if either the Riemannian or the finite dimensionality assumption is dropped.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension (Workshop)
Organizer(s):
Lorenzo Dello Schiavo (ISTA, Klosterneuburg)
Christian Ketterer (ALU Freiburg)
Chiara Rigoni (U of Vienna)