8 papers
Geometry of the subgaussian body of an isotropic convex body
Apostolos Giannopoulos, Minas Pafis, Natalia Tziotziou
For a centered convex body , let denote the symmetric convex body whose support function is given by the -norms of linear functionals on . Th…
Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures
Alexandros Eskenazis, Apostolos Giannopoulos, Natalia Tziotziou
This paper is dedicated to two geometric problems associated to log-concave measures on . First, we study the dimensional Brunn-Minkowski inequality for even log-conc…
Regular functional covering numbers
Apostolos Giannopoulos, Natalia Tziotziou
We establish the existence of a regular functional -position, in the sense of Pisier, for geometric log-concave functions. This provides a functional analogue of Pisier's regula…
Inequalities for sections and projections of log-concave functions
Natalia Tziotziou
We provide extensions of geometric inequalities about sections and projections of convex bodies to the setting of integrable log-concave functions. Namely, we consider suitable gen…
Moments of the Cramér transform of log-concave probability measures
Apostolos Giannopoulos, Natalia Tziotziou
Let be a centered log-concave probability measure on and let denote the Cramér transform of , i.e. $Î_μ^{\ast}(x)=\sup\{\langle x,ξ\rang…
On the maximal perimeter of isotropic log-concave probability measures
Silouanos Brazitikos, Apostolos Giannopoulos, Antonios Hmadi +1
We study the maximal perimeter constant of isotropic log-concave probability measures on . For a measure , this quantity, denoted by , is defined as the s…