Analysis and PDEs Seminar

Quantitative Faber-Krahn Inequalities and the ACF Monotonicity Formula

Speaker:  Robin Neumayer (Carnegie Mellon University)
Date:  Wednesday, 12 January 2022 - 15:00
Online: (ID: 814 9107 9139; Access code: 937701)


Among all drum heads of a fixed area, a circular drum head produces the vibration of lowest frequency. The general dimensional analogue of this fact is the Faber-Krahn inequality, which states that balls have the smallest principal Dirichlet eigenvalue among subsets of Euclidean space with a fixed volume. I will discuss new quantitative stability results for the Faber-Krahn inequality on Euclidean space, the round sphere, and hyperbolic space, as well as an application to the Alt-Caffarelli-Friedman monotonicity formula used in free boundary problems. This is based on joint work with Mark Allen and Dennis Kriventsov.