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On the Minimal Convex Shell of a Convex Body

Published online by Cambridge University Press:  20 November 2018

Carla Peri
Carla Peri*
Affiliation:
Istituto di Matematica Università Cattolica del Sacro Cuore Largo Gemelli, 1 20123 Milano Italy
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Abstract

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For any convex body C in ℝd we introduce the notion of the convex shell and we prove that there exists a unique "minimal" convex shell, extending the notion of the minimal spherical shell of C. Then we prove that a "typical" convex body touches the boundary of its minimal convex shell in precisely d + 2 points.

Keywords

52A2054E52convex bodyminimal convex shellBaire category
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 4 , 01 December 1993 , pp. 466 - 472
Copyright
Copyright © Canadian Mathematical Society 1993

References

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