Monatshefte für Mathematik

, Volume 126, Issue 1, pp 37–54

Section and projection means of convex bodies

  • Paul Goodey
  • Markus Kiderlen
  • Wolfgang Weil
Article

DOI: 10.1007/BF01312454

Cite this article as:
Goodey, P., Kiderlen, M. & Weil, W. Monatshefte für Mathematik (1998) 126: 37. doi:10.1007/BF01312454

Abstract

This paper is concerned with various geometric averages of sections or projections of convex bodies. In particular, we consider Minkowski and Blaschke sums of sections as well as Minkowski sums of projections. The main result is a Crofton-type formula for Blaschke sums of sections. This is used to establish connections between the different averages mentioned above. As a consequence, we obtain results which show that, in some circumstances, a convex body is determined by the averages of its sections or projections.

1991 Mathematics Subject Classification

52A20 Secondary 52A22 52A39 60D05 47G10 

Key words

convex body surface area measure Blaschke addition section mean projection mean Crofton formula spnerical integral transform 

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Paul Goodey
    • 1
  • Markus Kiderlen
    • 2
  • Wolfgang Weil
    • 2
  1. 1.Department of MathematicsUniversity of OklahomaNormanUSA
  2. 2.Mathematisches Institut IIUniversität KarlsruheKarlsruheGermany

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