26 citations · 27 across the 3 of their papers we have counts for
5 papers
Centroids of sections of convex bodies and Lusternik-Schnirelmann category
Julian Haddad, C. Hugo Jiménez, Rafael Villa
Given two symmetric convex bodies with strictly convex, we prove that there exist at least hyperplanes tangent to , such that the cent…
The sharp affine Sobolev trace inequality and variants
Pablo Luis De Nápoli, Julián Haddad, Carlos Hugo Jiménez +1
We establish a sharp affine Sobolev trace inequality by using the Busemann-Petty centroid inequality. For , our affine version is stronger than the famous sharp…
John's ellipsoid and the integral ratio of a log-concave function
David Alonso-Gutiérrez, Bernardo González Merino, Carlos Hugo Jiménez +1
We extend the notion of John's ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will e…
Rogers-Shephard inequality for log-concave functions
David Alonso-Gutiérrez, Bernardo González Merino, C. Hugo Jiménez +1
In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relati…
Push forward measures and concentration phenomena
C. Hugo JimÉnez, MÁrton NaszÓdi, Rafael Villa
In this note we study how a concentration phenomenon can be transmitted from one measure to a push-forward measure . In the first part, we push forward by $π:supp(μ)\rig…