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

Alonso Gutiérrez, David (Universidad de Zaragoza) ; González Merino, Bernardo ; Jiménez, Carlos Hugo ; Villa Rafael

Resumen: We 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.

Idioma: Inglés

DOI: 10.1007/s12220-017-9858-4

Año: 2018

Publicado en: JOURNAL OF GEOMETRIC ANALYSIS 28, 2 (2018), 1182-1201
ISSN: 1050-6926

Factor impacto JCR: 0.959 (2018)

Categ. JCR: MATHEMATICS rank: 103 / 313 = 0.329 (2018) - Q2 - T1

Factor impacto SCIMAGO: 1.62 - Geometry and Topology (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2013-42105-P
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2016-77710-P

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)