6 papers · 1 filter
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…
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 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…
Factoring Sobolev inequalities through classes of functions
David Alonso-Gutiérrez, Jesús Bastero, Julio Bernués
We recall two approaches to recent improvements of the classical Sobolev inequality. The first one follows the point of view of Real Analysis, while the second one relies on tools…
On the isotropy constant of projections of polytopes
David Alonso-Gutiérrez, Jesús Bastero, Julio Bernués +1
The isotropy constant of any -dimensional polytope with vertices is bounded by where is a numerical constant.