A characterization of the ellipsoid through planar grazes

Abstract

In this paper we proved the following: \emph{Let $K,L\subset {\mathbb{R}}^3$ be two $O$-symmetric convex bodies with $L\subset \text{int}K$ strictly convex. Suppose that from every $x$ in $\text{bd}K$ the graze $\Sigma (L,x)$ is a planar curve and $K$ is almost free with respect to $L$. Then $L$ is an ellipsoid.}

References in corpus (2)

• Two characterizations of ellipsoidal cones
• Sections and projections of nested convex bodies

Cited by in corpus (2)

• On characteristic properties of the ellipsoid in terms of circumscribed cones of a convex body
• Characterization of the sphere by means of congruent support cones