Fall 2021

Quantitative Faber-Krahn Inequalities and the ACF Monotonicity Formula

Friday, Oct. 1, 2021 2:00 pm2:40 pm PDT

Add to Calendar


Robin Neumayer (Northwestern University)


Calvin Lab Auditorium and Zoom

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.