1 citations · 1 across the 8 of their papers we have counts for
8 papers
On the Perelman-Pukhov quotient of successive radii: better and asymptotically optimal bounds
Bernardo González Merino, Beatriz Marín Gimeno, Mia Runge
Perel'man in 1987 and independently Pukhov in 1979 proved that the quotient between the -th successive outer radius and the -th successive inner radius of a convex body…
Minimization of the inradius of convex bodies for prescribed diameter and circumradius in Minkowski spaces
René Brandenberg, Bernardo González Merino, Mia Runge
We study Blaschke-Santaló diagrams for the inradius, circumradius, and diameter in arbitrary-dimensional Minkowski spaces. Their boundary parts are regularly described by four line…
On isoperimetric local-Bollobás-Thomason inequalities
Luis J. Alías, Bernardo González Merino, Beatriz Marín Gimeno
We prove the following isoperimetric-type inequality: for every convex body in and some there exists a suitable Hanner polytope …
On local Liakopoulos-Meyer type inequalities and their functional counterparts
Luis J. Alías, Bernardo González Merino, Beatriz Marín Gimeno
We provide a functional Rogers-Shephard type inequality for log-concave functions on and any -reducible -cover of . As a consequence, we derive a sharp loc…
Central diagonal sections of Gaussian cubes
Ferenc Fodor, Bernardo González Merino
The investigation of the volume, surface area, and other geometric properties of sections of convex bodies, and in particular cubes, has a long history and a rich literature. Howev…
A complete system of inequalities for the diameter, in-, and circumradius in the 3-dimensional Euclidean space
René Brandenberg, Bernardo González Merino, Mia Runge
We present a complete system of inequalities for the inradius, circumradius, and diameter in the -dimensional Euclidean space. To do so, we prove quasiconcavity of the inradius…
Narrowing the gaps of the missing Blaschke-Santaló diagrams
Bernardo González Merino
We solve several new sharp inequalities relating three quantities amongst the area, perimeter, inradius, circumradius, diameter, and minimal width of planar convex bodies. As a con…
Hunting for reduced polytopes
Bernardo González Merino, Thomas Jahn, Gerd Wachsmuth
By correcting an example by Polyanskii, we show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the…