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Minkowski surface area under affine transformations

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Rolf Clack
Rolf Clack
Affiliation:
Mathematisches Institut der Albert-Ludwigs-Universität, Hebelstrasse 29, 7800 Freiburg im Br., Germany.
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Extract

A convex compact subset of ℝd is called a convex body. The (Euclidean) surface area and volume of a convex body K are denoted s(K) and v(K) respectively. The support function of a convex body K is denned by h(K, x) = maxy∈K xty and the polar dual of K is given by K0 = {x: |xty|1, y∈K}. Double vertical bars shall denote the Euclidean length of a vector , and S shall denote the unit sphere (the Euclidean unit ball): S = {x: ║x║≤1}. We use for the mixed volume

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 232 - 238
Copyright
Copyright © University College London 1990

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