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PARALLEL BODIES AND NORMALS OF CONVEX BODIES

Part of: General convexity

Published online by Cambridge University Press:  13 December 2010

H. Groemer
H. Groemer*
Affiliation:
Department of Mathematics, The University of Arizona, Tucson, AZ 85721, U.S.A. (email: [email protected])
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Abstract

The primary aim of this paper is to determine how two convex bodies are related if their respective normal bundles are equal or, in a certain sense, close to each other. In connection with this problem some pertinent results concerning parallel bodies and the Steiner point are also discussed.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 57 , Issue 1 , January 2011 , pp. 109 - 119
Copyright
Copyright © University College London 2011

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References

[1]Bonnesen, T. and Fenchel, W., Theorie der konvexen Körper (Ergebnisse der Mathematik, Band 3), Springer (Berlin, 1934), Engl. transl.: Theory of Convex Bodies, BCS Assoc. (Moscow, ID, 1987).Google Scholar
[2]Groemer, H., Geometric Applications of Fourier Series and Spherical Harmonics, Cambridge University Press (Cambridge, 1996).CrossRefGoogle Scholar
[3]Groemer, H., Deviation measures and normals of convex bodies. Beiträge Algebra Geom. 45 (2004), 155–167.Google Scholar
[4]Schneider, R., Convex Bodies: The Brunn–Minkowski Theory, Cambridge University Press (Cambridge, 1993).CrossRefGoogle Scholar