Speaker
Sara Farinelli
(Università di Genova)
Description
The Payne–Weinberger inequality gives a sharp lower bound for the first non-zero Neumann eigenvalue of a convex domain in terms of its diameter. A recent result by Amato, Bucur and Fragalà provides a quantitative stability result in the Euclidean setting, based on a suitable convex partition argument. In this talk, I will present an approach to the problem in which convex partitions are replaced by needle decompositions in Euclidean space. This provides a natural framework for addressing the same question in non-flat settings, such the one of Riemannian manifolds with non-negative Ricci curvature, which will be also discussed. This is
based on ongoing joint work with N. De Ponti and I. Y. Violo.
Author
Sara Farinelli
(Università di Genova)