Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T04:14:01.683Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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