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