$L_p$ John ellipsoids for log-concave functions

Congli Yang; Fangwei Chen; Jianbo Fang; Miao Luo

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$L_p$ John ellipsoids for log-concave functions

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arxiv 2107.11018 v1 pith:CHTD7RUX submitted 2021-07-23 math.FA math.MG

Fangwei Chen , Jianbo Fang , Miao Luo , Congli Yang This is my paper · ORCID

classification math.FAmath.MG

keywords log-concavejohnellipsoidfunctionestablishedfunctionsanalogball

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abstract

The aim of this paper is to develop the $L_p$ John ellipsoid for the geometry of log-concave functions. Using the results of the $L_p$ Minkowski theory for log-concave function established in \cite{fan-xin-ye-geo2020}, we characterize the $L_p$ John ellipsoid for log-concave function, and establish some inequalities of the $L_p$ John ellipsoid for log-concave function. Finally, the analog of Ball's volume ratio inequality for the $L_p$ John ellipsoid of log-concave function is established.

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