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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
Volume inequalities for the i-th-convolution bodies
(Elsevier, 2015-04-01)
We obtain a new extension of Rogers-Sephard inequality providing an upper bound for the volume of the sum of two convex bodies K and L. We also give lower bounds for the volume of the k-th limiting convolution body of two ...
Artículo
An Lp-Functional Busemann–Petty Centroid Inequality
(Oxford Academic, 2020-01-23)
For a convex body K⊂Rn , let ΓpK be its Lp -centroid body. The Lp -Busemann–Petty centroid inequality states that vol(ΓpK)≥vol(K) , with equality if and only if K is an ellipsoid centered at the origin. In this ...
Artículo
Sampling quantum nonlocal correlations with high probability
(Springer, 2016-05)
It is well known that quantum correlations for bipartite dichotomic measurements are those of the form γ=(⟨ui,vj⟩)ni,j=1, where the vectors ui and vj are in the unit ball of a real Hilbert space. In this work we study the ...
Artículo
Sharp affine Sobolev type inequalities via the Lp Busemann–Petty centroid inequality
(Elsevier, 2016-07-15)
We show that the Lp Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev and Gagliardo-Nirenberg ...
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
Characterization of dual mixed volumes via polymeasures
(Elsevier, 2015-06-15)
We prove a characterization of the dual mixed volume in terms of functional properties of the polynomial associated to it. To do this, we use tools from the theory of multilinear operators on spaces of continuos functions. ...