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Extremal mean width when covering the 1-skeleton

Extremal mean width when covering the 1-skeleton For a given convex body K in ℝ d , let D n be the compact convex set of maximal mean width whose 1-skeleton can be covered by n congruent copies of K . Based on the fact that the mean width is proportional to the average perimeter of two-dimensional projections, it is proved that D n is close to being a segment for large n . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Oxford University Press

Extremal mean width when covering the 1-skeleton

Extremal mean width when covering the 1-skeleton

Bulletin of the London Mathematical Society , Volume 39 (6) – Dec 1, 2007

Abstract

For a given convex body K in ℝ d , let D n be the compact convex set of maximal mean width whose 1-skeleton can be covered by n congruent copies of K . Based on the fact that the mean width is proportional to the average perimeter of two-dimensional projections, it is proved that D n is close to being a segment for large n .

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References (9)

Publisher
Oxford University Press
Copyright
© 2007 London Mathematical Society
Subject
PAPERS
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdm081
Publisher site
See Article on Publisher Site

Abstract

For a given convex body K in ℝ d , let D n be the compact convex set of maximal mean width whose 1-skeleton can be covered by n congruent copies of K . Based on the fact that the mean width is proportional to the average perimeter of two-dimensional projections, it is proved that D n is close to being a segment for large n .

Journal

Bulletin of the London Mathematical SocietyOxford University Press

Published: Dec 1, 2007

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