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Shadow boundaries of typical convex bodies. measure properties

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Peter M. Gruber  and
Hartwig Sorger
Peter M. Gruber
Affiliation:
Abteilung fr Analysis, Technische Universitt Wien, Wiedner Hauptstrae 8-101142, A-1040 Vienna, Austria.
Hartwig Sorger
Affiliation:
Abteilung fr Analysis, Technische Universitt Wien, Wiedner Hauptstrajse 8-101142, A-1040 Vienna, Austria.
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Abstract

For a typical convex body in Ed a typical shadow boundary under parallel illumination has infinite (d - 2)-dimensional Hausdorff measurewhile having Hausdorff dimension d 2.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 36 , Issue 1 , June 1989 , pp. 142 - 152
Copyright
Copyright University College London 1989

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