On GLń(ℝ)-invariant classes of convex bodies

Semyon Alesker

doi:10.1112/S0025579300014789

On GLń(ℝ)-invariant classes of convex bodies

Semyon Alesker^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	57-61
Number of pages	5
Journal	Mathematika
Volume	50
Issue number	1-2
DOIs	https://doi.org/10.1112/S0025579300014789
State	Published - 2003

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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.",

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On GLń(ℝ)-invariant classes of convex bodies

Abstract

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