Pavlos Kalantzopoulos

We use the characterization of the case of equality in Barthe's Geometric Reverse Brascamp-Lieb inequality to characterize equality in Liakopoulos's volume estimate in terms of sections by certain lower-dimensional linear subspaces.

We consider a family of jointly Gaussian random vectors $\xi_j \in \mathbb{R}^{k_j}$, each standard normal but possibly correlated, and investigate when\[ \mathbb{E}\, F\!\Bigl(B\bigl(|T_{z_1} f_1(\xi_1)|,\dots,|T_{z_n}…

Let $\xi$ be the standard normal random vector in $\mathbb{R}^{k}$. Under some mild growth and smoothness assumptions on any increasing $P, Q : [0, \infty) \mapsto [0, \infty)$ we show $(P,Q)$ complex hypercontractivity $$ Q^{-1}(\mathbb{E}…

The works of Bennett, Carbery, Christ, Tao and of Valdimarsson have clarified when equality holds in the Brascamp-Lieb inequality. Here we characterize the case of equality in the Geometric case of Barthe's reverse Brascamp-Lieb inequality.

Let $k\geq 2$ be an integer. In the spirit of Kolesnikov-Werner \cite{KW}, for each $j\in\{2,\ldots,k\}$, we conjecture a sharp Santal\'{o} type inequality (we call it $j$-Santal\'{o} conjecture) for many sets (or more generally for many…

We prove the log-Brunn-Minkowski conjecture for convex bodies with symmetries to $n$ independent hyperplanes, and discuss the equality case and the uniqueness of the solution of the related case of the logarithmic Minkowski problem. We also…