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


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.


Authors’ Affiliations

Departamento de Análisis Matemático, Universidad de Alicante


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© 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.