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Corpus ID: 239998791

A new and simple proof of the false centre theorem

@inproceedings{Montejano2021ANA,
title={A new and simple proof of the false centre theorem},
author={Luis Pedro Montejano and Efr'en Morales-Amaya},
year={2021}
}

Theorem 1.1 was first proved in all its generality by D. G. Larman [4]. Theorem 1.3 was proved by C. A. Rogers [7], when p ∈ int K and by G. R. Burton in general (Theorem 2 of [2]). Theorem 1.2 was first proved by H. Brunn [1] under the hypothesis of regularity and in general by G. R. Burton [3] (see (3.3) and (3.6) of Petty’s survey [6]). For more about characterization of ellipsoids see [8] and Section 2.12 of [5]. We need some notation. Let K be a convex body in euclidean 3-space R, let p… Expand

If K is a set in n -dimensional Euclidean space E n , n ≥ 2, with non-empty interior, then a point p of E n is called a pseudo-centre of K provided tha each two dimensional flat through p intersects… Expand

This is a survey on various characteristic properties of ellipsoids and convex quadrics in the family of convex hypersurfaces in $${\mathbb {R}}^n$$Rn. The topics under consideration include planar… Expand