8 papers · 1 filter
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…
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 supr…
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…
Sections and projections of the outer and inner regularizations of a convex body
Natalia Tziotziou
We establish new geometric inequalities comparing the volumes of sections and projections of a convex body, whose barycenter or Santaló point is at the origin, with those of its in…
On the deterministic interior body of random polytopes
Minas Pafis, Natalia Tziotziou
Let be a sequence of independent copies of a random vector in . We revisit the question to determine the asymptotic shape of the random p…