7 papers
Volume and Projection Inequalities II: Determinants and -Sums
Matthieu Fradelizi, Auttawich Manui, Cheikh Saliou Ndiaye +1
We study inequalities for the volume of orthogonal projections and their relation to Firey -sum, together with their determinant-power analogues, motivated by the Dembo--Cover…
Volume and Projection Inequalities I: Zonoids and Courtade's Conjecture
Matthieu Fradelizi, Alfredo Hubard, Auttawich Manui +3
We study volume and projection inequalities for zonoids through the multiaffine determinant polynomials that encode their volumes. We show that a log-submodularity conjecture for t…
Integral inequalities for -convolutions of -concave functions
Mokshay Madiman, Auttawich Manui, Bartłomiej Zawalski +1
Classical sumset inequalities originating in additive combinatorics admit geometric analogues for convex bodies in finite-dimensional real vector spaces, as recently developed by F…
On the Fourier Mean Bodies of a Convex Body
Dylan Langharst, Auttawich Manui, Artem Zvavitch
In 1998, R. Gardner and G. Zhang introduced the radial th mean bodies of a convex body , , which have since become important objects in geometr…
Geometric Large-Deviation-Type Principles for Mixed Measures
Malak Lafi, Artem Zvavitch
We study a geometric analogue of the large deviation principle for mixed measures associated with a class of -concave probability measures whose densities depend on the gauge…
Measure comparison problems for dilations of convex bodies
Malak Lafi, Artem Zvavitch
We study a version of the Busemann-Petty problem for -concave measures with an additional assumption on the dilates of convex, symmetric bodies. One of our main tools is an a…