Convex bodies with many elliptic sections

2014/08/25 by Isaac Arelio, Arelio, Isaac, Luis Montejano +1
Mathematics · #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1408.5647

Abstract

We show in this paper that two normal elliptic sections through every point of the boundary of a smooth convex body essentially characterize an ellipsoid and furthermore, that four different pairwise non-tangent elliptic sections through every point of the C²-differentiable boundary of a convex body also essentially characterize an ellipsoid.

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