16 citations · 45 across the 24 of their papers we have counts for
14 papers · 1 filter
A strengthening of the Blaschke-Santaló inequality for -symmetric planar convex bodies
Károly J. Böröczky, Endre Makai
We verify the inequality for any -symmetric convex body where is either the John ellipse of maximal ar…
On Ball's conjectured Santaló type inequality
Károly J. Böröczky, Konstantinos Patsalos, Christos Saroglou
We prove that if is a symmetric and isotropic convex body in , then $$\int_K\langle x,u\rangle^2\,dx\int_{K^\circ}\langle x,u\rangle^2\,dx\leq \left(\int_{B_2^n}\…
Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality
Karoly J. Böröczky, Ferenc Fodor, 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 sec…
The Brascamp-Lieb inequality in Convex Geometry and in the Theory of Algorithms
Károly J. Böröczky
The Brascamp-Lieb inequality in harmonic analysis was proved by Brascamp and Lieb in the rank one case in 1976, and by Lieb in 1990. It says that in a certain inequality, the optim…
Convex bodies of constant width in spaces of constant curvature and the extremal area of Reuleaux triangles
Karoly J. Boroczky, Adam Sagmeister
Extending Blaschke and Lebesgue's classical result in the Euclidean plane, it has been recently proved in spherical and the hyperbolic cases, as well, that Reuleaux triangles have…
Reverse Alexandrov--Fenchel inequalities for zonoids
Károly J. Böröczky, Daniel Hug
The Alexandrov--Fenchel inequality bounds from below the square of the mixed volume of convex bodies in by the product o…