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Characterization of ellipsoids and polarity in convex sets

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Luis Montejano  and
Efren Morales
Luis Montejano
Affiliation:
Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, Mexico, D.F.C.P. 04510.
Efren Morales
Affiliation:
Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, Ciudad Universitaria, Mexico, D.F.C.P. 04510.
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Abstract

By introducing the concept of polarity in convex sets, it is possible, in a natural way, to generalize several classic characterizations of ellipsoids, showing that all of them depend upon and are related to the concept of projective centre of symmetry. Using these ideas, it is also possible to develop new characterizations of ellipsoids and to propose new problems.

MSC classification

Secondary: 52A30: Variants of convex sets (star-shaped, ($m, n$)-convex, etc.)
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 63 - 72
Copyright
Copyright © University College London 2003

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