John’s Ellipsoid and the Integral Ratio of a Log-Concave Function |
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| Authors: | David Alonso-Gutiérrez Bernardo González Merino C Hugo Jiménez Rafael Villa |
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| Institution: | 1.Universidad de Zaragoza,Zaragoza,Spain;2.University Centre of Defence at the Spanish Air Force Academy, MDE-UPCT,Murcia,Spain;3.Pontifícia Universidade Católica do Rio de Janeiro,Rio de Janeiro,Brazil;4.Universidad de Sevilla,Sevilla,Spain |
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| Abstract: | 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 we will find the log-concave function maximizing the integral ratio. A reverse functional affine isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality. |
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