3 may 2022 -- 16:00
Differential Geometry Seminar Torino (online)
Abstract.
We consider the isoperimetric problem on Riemannian manifolds with nonnegative Ricci curvature and Euclidean volume growth, i.e., such that the volume of balls grows like the one of Euclidean ones as the radius diverges. The problem aims at minimizing the perimeter among sets having a fixed volume. Under an additional natural assumption on asymptotic cones to the manifold, we prove the existence of isoperimetric sets for any sufficiently large volume. The existence result holds without additional assumptions on manifolds with nonnegative sectional curvature.
The proof builds on an asymptotic mass decomposition result for minimizing sequences, on a sharp isoperimetric inequality, and on concavity properties of the isoperimetric profile.
More generally, the results hold on $N$-dimensional ${\rm RCD}(0,N)$ metric measure spaces, which are spaces having Ricci curvature bounded from below by zero in a generalized sense.
The results mentioned are contained in works in collaboration with G. Antonelli, E. Bruè, M. Fogagnolo, E. Pasqualetto, and D. Semola.
----------------------------------------------------------------------------------
The link of the virtual room will be sent one day before the talk to all registered participants. To register, please send an e-mail to dgseminar.torino@gmail.com