Analysis and PDEs Seminar
Quantitative Faber-Krahn Inequalities and the ACF Monotonicity Formula
Speaker: Robin Neumayer (Carnegie Mellon University)Date: Wednesday, 12 January 2022 - 15:00Online: us06web.zoom.us/j/81491079139?pwd=OWo1TWc0NEExNDJZUFljWVRIdkZRQT09 (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.