8 papers
On affine invariant and local Loomis-Whitney type inequalities
David Alonso-Gutiérrez, Julio Bernués, Silouanos Brazitikos +1
We prove various extensions of the Loomis-Whitney inequality and its dual, where the subspaces on which the projections (or sections) are considered are either spanned by vectors $…
An extension of Berwald's inequality and its relation to Zhang's inequality
David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino
In this note prove the following Berwald-type inequality, showing that for any integrable log-concave function and any concave function $h:L\ri…
Soñando con números, María Andresa Casamayor (1720-1780)
Julio Bernués, Pedro J. Miana
María Andresa Casamayor de la Coma, born in Zaragoza, is known as the first woman who published a scientific book in Spain. In this paper we provide answers to several of the most…
Zhang's inequality for log-concave functions
David Alonso-Gutiérrez, Julio Bernués, Bernardo González Merino
Zhang's reverse affine isoperimetric inequality states that among all convex bodies , the affine invariant quantity (where deno…
The square negative correlation on l_p^n balls
David Alonso-Gutiérrez, Julio Bernués
In this paper we prove that for any the unit ball, , satisfies the square negative correlation property with respect to every orthonormal basis,…
The variance conjecture on projections of the cube
David Alonso-Gutiérrez, Julio Bernués
We prove that the uniform probability measure on every -dimensional projection of the -dimensional unit cube verifies the variance conjecture with an absolute constan…