25 citations · 32 across the 7 of their papers we have counts for
11 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…
Stone-Weierstrass theorem for homogeneous polynomials and its role in convex geometry
Bernardo González Merino, Rafael Villa
We give a uniform approximation of the characteristic function of the boundary of a centrally symmetric n-dimensional compact and convex set by homogeneous polynomials of even degr…
Best approximation of functions by log-polynomials
David Alonso-Gutiérrez, Bernardo González Merino, Rafael Villa
Lasserre [La] proved that for every compact set and every even number there exists a unique homogeneous polynomial of degree with $K\subset G_1(…
Some remarks on Petty projection of log-concave functions
Leticia Alves da Silva, Bernardo González Merino, Rafael Villa
In this note we study the Petty projection of a log-concave function, which has been recently introduced in [9]. Moreover, we present some new inequalities involving this new notio…
Rogers-Shephard and local Loomis-Whitney type inequalities
David Alonso-Gutiérrez, Shiri Artstein-Avidan, Bernardo González Merino +2
We provide functional analogues of the classical geometric inequality of Rogers and Shephard on products of volumes of sections and projections. As a consequence we recover (and ob…
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…