000079510 001__ 79510 000079510 005__ 20191122145057.0 000079510 0247_ $$2doi$$a10.1007/s12220-017-9858-4 000079510 0248_ $$2sideral$$a98820 000079510 037__ $$aART-2018-98820 000079510 041__ $$aeng 000079510 100__ $$0(orcid)0000-0003-1256-3671$$aAlonso Gutiérrez, David$$uUniversidad de Zaragoza 000079510 245__ $$aJohn's ellipsoid and the integral ratio of a log-concave function 000079510 260__ $$c2018 000079510 5060_ $$aAccess copy available to the general public$$fUnrestricted 000079510 5203_ $$aWe extend the notion of John’s ellipsoid to the setting of integrable logconcave 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. 000079510 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2013-42105-P$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P 000079510 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000079510 590__ $$a0.959$$b2018 000079510 591__ $$aMATHEMATICS$$b103 / 313 = 0.329$$c2018$$dQ2$$eT1 000079510 592__ $$a1.62$$b2018 000079510 593__ $$aGeometry and Topology$$c2018$$dQ1 000079510 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000079510 700__ $$aGonzález Merino, Bernardo 000079510 700__ $$aJiménez, Carlos Hugo 000079510 700__ $$aVilla Rafael 000079510 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000079510 773__ $$g28, 2 (2018), 1182-1201$$pJ. geom. anal.$$tJOURNAL OF GEOMETRIC ANALYSIS$$x1050-6926 000079510 8564_ $$s341986$$uhttps://zaguan.unizar.es/record/79510/files/texto_completo.pdf$$yPostprint 000079510 8564_ $$s69690$$uhttps://zaguan.unizar.es/record/79510/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000079510 909CO $$ooai:zaguan.unizar.es:79510$$particulos$$pdriver 000079510 951__ $$a2019-11-22-14:46:53 000079510 980__ $$aARTICLE