2 citations · 4 across the 22 of their papers we have counts for
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The Brunn-Minkowski inequality for the first eigenvalue of the Ornstein-Uhlenbeck operator and log-concavity of the relevant eigenfunction
Andrea Colesanti, Elisa Francini, Galyna Livshyts +1
We prove that the first (nontrivial) Dirichlet eigenvalue of the Ornstein-Uhlenbeck operator as a function of the domain, is convex with r…
Kohler-Jobin meets Ehrhard: the sharp lower bound for the Gaussian principal frequency while the Gaussian torsional rigidity is fixed, via rearrangements
Orli Herscovici, Galyna V. Livshyts
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-Jobi…
On the -Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures
Johannes Hosle, Alexander V. Kolesnikov, Galyna V. Livshyts
We study several of the recent conjectures in regards to the role of symmetry in the inequalities of Brunn-Minkowski type, such as the -Brunn-Minkowski conjecture of Böröczky,…
On the Gardner-Zvavitch conjecture: symmetry in the inequalities of Brunn-Minkowski type
Alexander V. Kolesnikov, Galyna V. Livshyts
In this paper, we study the conjecture of Gardner and Zvavitch from \cite{GZ}, which suggests that the standard Gaussian measure enjoys -concavity with respect to…