Open Access

Comparing the relative volume with the relative inradius and the relative width

Journal of Inequalities and Applications20062006:54542

DOI: 10.1155/JIA/2006/54542

Received: 28 February 2006

Accepted: 29 August 2006

Published: 19 December 2006

Abstract

We consider subdivisions of a convex body in two subsets and . We obtain several inequalities comparing the relative volume: (1) with the minimum relative inradius, (2) with the maximum relative inradius, (3) with the minimum relative width, and (4) with the maximum relative width. In each case, we obtain the best upper and lower estimates for subdivisions determined by general hypersurfaces and by hyperplanes.

[12345]

Authors’ Affiliations

(1)
Departamento de Análisis Matemático, Universidad de Alicante

References

  1. Cerdán A, Miori C, Segura Gomis S: Relative isodiametric inequalities. Beiträge zur Algebra und Geometrie 2004,45(2):595–605.MATHGoogle Scholar
  2. Cerdán A, Schnell U, Segura Gomis S: On relative geometric inequalities. Mathematical Inequalities & Applications 2004,7(1):135–148.MathSciNetView ArticleMATHGoogle Scholar
  3. Cianchi A: On relative isoperimetric inequalities in the plane. Bollettino della Unione Matemàtica Italiana. Serie VII. B 1989,3(2):289–325.MathSciNetMATHGoogle Scholar
  4. Pál J: Ein Minimumproblem für Ovale. Mathematische Annalen 1921,83(3–4):311–319. 10.1007/BF01458387MathSciNetView ArticleMATHGoogle Scholar
  5. Peri C: On relative isoperimetric inequalities. Conferenze del Seminario di Matematica dell'Università di Bari 2001, (279):14.Google Scholar

Copyright

© A. Cerdán 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.