# Kohler-Jobin meets Ehrhard: the sharp lower bound for the Gaussian principal frequency while the Gaussian torsional rigidity is fixed, via rearrangements

@inproceedings{Herscovici2022KohlerJobinME, title={Kohler-Jobin meets Ehrhard: the sharp lower bound for the Gaussian principal frequency while the Gaussian torsional rigidity is fixed, via rearrangements}, author={Orli Herscovici and Galyna V. Livshyts}, year={2022} }

Abstract. In this note, we provide an adaptation of the Kohler-Jobin rearrangement technique to the setting of the Gauss space. As a result, we prove the Gaussian analogue of the Kohler-Jobin’s resolution of a conjecture of PólyaSzegö: 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…

## References

SHOWING 1-10 OF 23 REFERENCES

Extremal properties of half-spaces for spherically invariant measures

- Mathematics
- 1978

Below we shall establish certain extremal properties of half-spaces for spherically symmetrical and, in particular, Gaussian (including infinite-dimensional) measures: we also prove inequalities for…

A Short Course on Rearrangement Inequalities

- Mathematics
- 2009

These notes grew out of introductory courses for graduate students that I gave at the First IMDEA Winter School in Madrid in January 2009, and at the Universita di Napoli “Federico II” in April 2009.…

Minimal rearrangements of Sobolev functions.

- Mathematics
- 1987

where α (n) is the volume of the unit η-ball in H$ and μ(ί)< oo is the Lebesgue measure of the set Et = {x: u(x)>t}. Note that μ(ι) = \Ε*\ where E* = {x: ii*(x)>f} and |E*| denotes the Lebesgue…

On the cases of equality in Bobkov's inequality and Gaussian rearrangement

- Mathematics
- 1999

Abstract. We determine all of the cases of equality in a recent inequality of Bobkov that implies the isoperimetric inequality on Gauss space. As an application we determine all of the cases of…

Éléments extrémaux pour les inégalités de Brunn-Minkowski gaussiennes

- Mathematics
- 1986

On etudie les ensembles pour lesquels l'egalite est atteinte dans les inegalites de C. Borell et de Brunn-Minkowski gaussienne en dimension finie. On caracterise aussi les fonctions telles que…

Beweis

- Law
- 2019

Volume 4 of the series „Baden-Badener Strafrechtsgespräche“ [Baden-Baden talks on criminal law] includes the 20 presentations given at the interdisciplinary conference on the subject of “proof” on…

Isoperimetric inequalities in mathematical physics

- Physics, Mathematics
- 1951

The description for this book, Isoperimetric Inequalities in Mathematical Physics. (AM-27), will be forthcoming.

Analysis

- Computer ScienceMachine Translation
- 2004

The parser, especially its mapping rule interpreter, used in KBMT-89 is described, characterized by its ability to produce semantic and syntactic structures of a parse simultaneously and therefore more efficiently than other kinds of analyzers.

On torsional rigidity and principal frequencies: an invitation to the Kohler-Jobin rearrangement technique

- Mathematics
- 2014

We generalize to the p -Laplacian
Δ p a spectral inequality proved by M.-T.
Kohler−Jobin. As a particular case of such a generalization, we obtain a sharp lower bound
on the first Dirichlet…