arXiv subjects

C. Hugo Jimenez

Publications and source records attributed to C. Hugo Jimenez.

3 recordsLinked to original sources

arXiv2018

Asymmetric Blaschke-Santaló functional inequalities

In this work we establish functional asymmetric versions of the celebrated Blaschke-Santaló inequality. As consequences of these inequalities we recover their geometric counterparts with equality cases, as well as, another inequality with strong probabilistic flavour that was firstly obtained by Lutwak, Yang and Zhang. We present a brief study on an $L_p$ functional analogue to the center of mass that is necessary for our arguments and that might be of independent interest.

math.MG↗

arXiv2016

Sharp affine Sobolev type inequalities via the $\Lp$ Busemann-Petty centroid inequality

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 inequalities. Our approach allows also to characterize directly the corresponding equality cases.

math.FA↗

arXiv2013

Brunn-Minkowski and Zhang inequalities for Convolution Bodies

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 on Convex Geometry involving convolution bodies or polar projection bodies. The extension of this new version to more than two sets is also given.

math.FA↗