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arXiv · 2207.13294

A characterization of the ellipsoid through planar grazes

Ivan Gonzalez Garcia·Jesus Jeronimo Castro·Diana Janett Verdusco Hernandez·Efren Morales Amaya
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Abstract

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

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Ivan Gonzalez Garcia, Jesus Jeronimo Castro, Diana Janett Verdusco Hernandez, Efren Morales Amaya. 2022-07-27. A characterization of the ellipsoid through planar grazes. https://doi.org/10.1112/mtk.12176

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