John's ellipsoid and the integral ratio of a log-concave function

2018-11-192018-11-192018-04Alonso Gutiérrez, D., González Merino, B., Jiménez Gómez, C.H. y Villa Caro, R. (2018). John's ellipsoid and the integral ratio of a log-concave function. Journal of Geometric Analysis, 28 (2), 1182-1201.1050-69261559-002xhttps://hdl.handle.net/11441/80347We 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Log-concave functionJohn’s positionVolume ratioReverse affine isoperimetric inequalityJohn's ellipsoid and the integral ratio of a log-concave functioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.1007/s12220-017-9858-4