48 citations · 91 across the 23 of their papers we have counts for
8 papers · 1 filter
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…
Weak -nets for polynomial superlevel sets
Pablo González-Mazón, Alfredo Hubard, Roman Karasev
We prove that for any Borel probability measure on there exists a set of points such that any -variate quadratic polynomial th…
Systolic inequalities for the number of vertices
Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard +1
Inspired by the classical Riemannian systolic inequality of Gromov we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in…
Equipartitions and Mahler volumes of symmetric convex bodies
Matthieu Fradelizi, Alfredo Hubard, Mathieu Meyer +2
Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular,…
Realization spaces of arrangements of convex bodies
Michael Gene Dobbins, Andreas Holmsen, Alfredo Hubard
We introduce combinatorial types of arrangements of convex bodies, extending order types of point sets to arrangements of convex bodies, and study their realization spaces. Our mai…
Regular systems of paths and families of convex sets in convex position
Michael G. Dobbins, Andreas F. Holmsen, Alfredo Hubard
In this paper we show that every sufficiently large family of convex bodies in the plane has a large subfamily in convex position provided that the number of common tangents of eac…
Convex Equipartitions: The Spicy Chicken Theorem
Roman Karasev, Alfredo Hubard, Boris Aronov
We show that, for any prime power n and any convex body K (i.e., a compact convex set with interior) in Rd, there exists a partition of K into n convex sets with equal volumes and…
Convex Equipartitions of volume and surface area
Boris Aronov, Alfredo Hubard
We show that, for any prime power p^k and any convex body K (i.e., a compact convex set with interior) in Rd, there exists a partition of K into p^k convex sets with equal volume a…