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Isoperimetric problems for polytopes with a given number of vertices

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Károly Böröczky  and
Károly Böröczky Jr.
Károly Böröczky
Affiliation:
Math. Inst. Hung. Acad. Sci., Budapest, Pf. 127, 1364 Hungary.
Károly Böröczky Jr.
Affiliation:
Math. Inst. Hung. Acad. Sci., Budapest, Pf. 127, 1364 Hungary.
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Extract

The prototype of isoperimetric problems is to minimize the surface area of a convex body with given volume. The minimal body is naturally the suitable ball. The solution to this problem in the planar case was already known to the ancient Greeks. In the higher dimensional cases, the first proofs were provided with the help of Steiner's symmetrization method towards the end of the last century. Important later contributors are, among others, Minkowski, Blaschke, Hadwiger. By their work, the optimality of the ball has been also verified for a much wider class of sets (see [14]).

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 43 , Issue 2 , December 1996 , pp. 237 - 254
Copyright
Copyright © University College London 1996

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