A Characterization of the sphere and a body of revolution by means of Larman points

María Angeles Alfonseca, Michelle Cordier, Jesús Jerónimo-Castro +1

Let $K\subset {\mathbb{R}}^n$, $n\ge 3$, be a convex body. A point $p$ the interior of $K$ is said to be a Larman point of $K$ if for every hyperplane $\Pi$ passing through $p$ the se…