BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Characterizations of the sphere by means of visual cones: an alternative proof of Matsuura's theorem Amaya, Efren Morales

Description

In this work we prove that if there exists a point $p\in \mathbb{R}^n$ and a smooth convex body $M$ in $\mathbb{R}^n$, $n\geq 3$, contained in the interior of the unit ball of $\mathbb{R}^n$, such that $M$ looks centrally symmetric, and $p$ appears as the centre, from each point of $\mathbb{S}^{n-1}$, then $M$ is an sphere. Using this result we derived, straightaway, a well known characterization of the sphere due to S. Matsuura

Item Media

Item Citations and Data

Rights

Attribution-NonCommercial-NoDerivatives 4.0 International