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Sausage-skin problems for finite coverings

Published online by Cambridge University Press:  26 February 2010

Gábor Fejes Tóth ,
Peter Gritzmann  and
Jörg M. Wills
Gábor Fejes Tóth
Affiliation:
Math. Inst. Hungar. Acad. Sciences, Reáltanoda u. 13–15, H-1053 Budapest.
Peter Gritzmann
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstrasse, 3, D-5900, Siegen, W. Germany.
Jörg M. Wills
Affiliation:
Math. Inst. Univ. Siegen, Hölderlinstrasse, 3, D-5900, Siegen, W. Germany.
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Extract

Let denote the set of convex bodies of Ed, i.e. the set of all compact convex subsets of Ed. Let Bi be the unit i-ball, ωi its volume and Si-1 the unit sphere bd Bi. For an arbitrary denote the j-th quermassintegral (for definition and properties compare [7]). A different normalization of the functionals Wo, …, Wd leads to the intrinsic volumes Vj (which were introduced in [9]) defined by The intrinsic volumes are independent of the dimension of the space in which K is embedded. In particular, V0(K) = 1, Vd-1 (K) is half the surface area of K and Vd{K) = V(K) is its volume.

Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 117 - 136
Copyright
Copyright © University College London 1984

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References

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