Existence of Gauss John ellipsoid operator problem

Abstract

There is a common example in convex geometry and Banach space geometry: the unique ellipsoid with the largest volume associated with each symmetric convex body K is called John ellipsoid. In this paper, we will give some results of John ellipsoid operator problem with Gaussian measure, mainly the continuity of Gaussian measure and the existence of ellipsoid operator.

Keywords

• convex geometry
• symmetric convex body
• john ellipsoid
• gaussian measure