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On GLn(ℝ)-invariant classes of convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Semyon Alesker
Semyon Alesker
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv 69978, Tel Aviv, Israel. E-mail: semyon@post.tau.ac.il
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Abstract

A generalization of the following two facts is proved: the class of generalized zonoids is dense in the class of convex compact bodies with a centre of symmetry, and the class of generalized triangle bodies is dense in the class of all convex compact bodies (proved by Schneider). The main result is deduced from a more general representation theoretical statement.

MSC classification

Secondary: 52A27: Approximation by convex sets
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 57 - 61
Copyright
Copyright © University College London 2003

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