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Asymmetry-Unified Volume Bounds for Extremal k-Ellipsoids in Convex Geometry

Sharp inequalities bounding the volume of the largest k-ellipsoid inscribed in a convex body (relative to its John ellipsoid) and the smallest k-ellipsoid containing a projection (relative to its Loewner ellipsoid), using the John asymmetry to unify the general and centrally-symmetric cases into single tight bounds.

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2501.00653

Studies volume-extremal k-dimensional ellipsoids attached to an n-dimensional convex body: the maximal-volume k-ellipsoid inscribed in the body (bounded in terms of its John ellipsoid, the volume-max…