## An adaptation of Kohler-Jobin rearrangement technique with fixed torsional rigidity to the Gaussian space

Series
Analysis Seminar
Time
Wednesday, January 26, 2022 - 2:00pm for 1 hour (actually 50 minutes)
Location
Speaker
Orli Herscovici – Georgia Tech – oherscovici3@gatech.edu
Organizer

In this talk, we show an adaptation of the Kohler-Jobin rearrangement technique to the setting of the Gauss space. As a result, we present the Gaussian analogue of the Kohler-Jobin's resolution of a conjecture of Polya-Szego: when the Gaussian torsional rigidity of a (convex) domain is fixed, the Gaussian principal frequency is minimized for the half-space. At the core of this rearrangement technique is the idea of considering a modified''  torsional rigidity, with respect to a given function, and rearranging its layers to half-spaces, in a particular way; the Rayleigh quotient decreases with this procedure.