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Estimating sizes of a convex body by successive diameters and widths

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

U. Betke  and
M. Henk
U. Betke
Affiliation:
Mathematisches Institut, Universität Siegen, Hōlderlinstrasse 3, D-W-5900, Siegen, Germany.
M. Henk
Affiliation:
Mathematisches Institut, Universität Siegen, Hölderlinstrasse 3, D-W-5900, Siegen, Germany.
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Abstract

The second theorem of Minkowski establishes a relation between the successive minima and the volume of a 0-symmetric convex body. Here we show corresponding inequalities for arbitrary convex bodies, where the successive minima are replaced by certain successive diameters and successive widths.

We further give some applications of these results to successive radii, intrinsic volumes and the lattice point enumerator of a convex body.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 39 , Issue 2 , December 1992 , pp. 247 - 257
Copyright
Copyright © University College London 1992

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