Isoperimetry and geometric rigidity on manifolds with nonnegative curvature
speaker: Marco Pozzetta (Università di Pisa)abstract: The isoperimetric problem on a Riemannian manifold aims at minimizing the measure of the boundary, called perimeter, among subsets having a given volume. The isoperimetric profile is the function assigning to any volume the infimum of the problem. The aim of this talk is to discuss connections between bounds on the isoperimetric profile and geometric rigidities on noncompact manifolds with nonnegative curvature. We shall present: (i) an isoperimetric inequality on manifolds with nonnegative Ricci curvature and large volume growth, discussing its rigidity; (ii) rigidity results in terms of upper bounds on the isoperimetric profile on manifolds with nonnegative sectional curvature and linear volume growth. The proofs exploit tools and methods from the theory of metric measure spaces with lower curvature bounds. The talk is based on works in collaboration with G. Antonelli, E. Bru`e, M. Fogagnolo, S. Nardulli, E. Pasqualetto, D. Semola, and I. Y. Violo.
timetable:
Fri 22 Sep, 11:20 - 12:20, Aula Dini
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