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Artículo
John's ellipsoid and the integral ratio of a log-concave function
(Springer, 2018-04)
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 extend the notion of volume ratio, and ...
Artículo
Maximal equilateral sets
(Springer, 2013-09)
A subset of a normed space X is called equilateral if the distance between any two points is the same. Let m(X) be the smallest possible size of an equilateral subset of X maximal with respect to inclusion. We first observe ...
Tesis Doctoral
Propiedades de concentración en espacios de dimensión finita Inmersiones isométricas en espacios de funciones continuas
(1998)
Esta memoria está dedicada al estudio de dos problemas del Análisis Funcional: El estudio de propiedades de concentración y su relación con la Geometría de los Espacios de Banach, englobado dentro de la Teoría Local de ...
Artículo
Rogers-Shephard inequality for log-concave functions
(Elsevier, 2016-12-01)
In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and ...
Artículo
Brunn-Minkowski and Zhang inequalities for convolution bodies
(Elsevier, 2013-05-01)
A quantitative version of Minkowski sum, extending the definition of θ-convolution of convex bodies, is studied to obtain extensions of the Brunn-Minkowski and Zhang inequalities, as well as, other interesting properties ...
Artículo
A lower bound for the equilateral number of normed spaces
(American Mathematical Society, 2008)
We show that if the Banach-Mazur distance between an n-dimensional normed space X and ℓ n∞ is at most 3/2, then there exist n + 1 equidistant points in X. By a well-known result of Alon and Milman, this implies that an ...
Artículo
Concentration of the distance in finite dimensional normed spaces
(University College London, Faculty of Mathematical and Physical Sciences, Department of Mathematics, 1998-12)
We prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ∥x − y∥ is more than √2(1 − ε). As a consecuence, we obtain a result proved by Bourgain, using QS-descomposition, ...