Ellipsoid characterization theorems

Lángi, Zsolt (2013) Ellipsoid characterization theorems. Advances in Geometry, 13 (1). pp. 145-154. ISSN 1615-7168


Download (173kB) | Preview


In this note we prove two ellipsoid characterization theorems. The first one is that if K is a convex body in a normed space with unit ball M, and for any point p ∉ K and in any 2-dimensional plane P intersecting intK and containing p, there are two tangent segments of the same normed length from p to K, then K and M are homothetic ellipsoids. Furthermore, we show that if M is the unit ball of a strictly convex, smooth norm, and in this norm billiard angular bisectors coincide with Busemann angular bisectors or Glogovskij angular bisectors, then M is an ellipse.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria
Depositing User: Dr. Zsolt Lángi
Date Deposited: 11 Sep 2015 09:59
Last Modified: 03 Apr 2023 08:31

Actions (login required)

Edit Item Edit Item