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Chord power integrals and radial mean bodies

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
342
Issue
1
Identifiers
DOI: 10.1016/j.jmaa.2007.12.033
Keywords
  • Convex Body
  • Dual Quermassintegrals
  • Chord Power Integrals
  • Radial Mean Body
Disciplines
  • Mathematics

Abstract

Abstract In this paper, we obtain a formula relating the chord power integrals of a convex body K and the dual quermassintegrals of its radial pth mean body R p K . With this, a relation among the chord power integrals of a convex body K under dilation transformations is found. As an interesting application, some geometric inequalities between the dual quermassintegrals of R p K and the volume of K, which are equivalent to the isoperimetric-type inequalities of chord power integrals, are also established.

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