Journal of Inequalities and Applications 
Volume 2006 (2006), Article ID 54542, 8 pages
doi:10.1155/JIA/2006/54542

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

A. Cerdán

 Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, Alicante 03080, Spain
Received 28 February 2006; Revised 24 August 2006; Accepted 29 August 2006

Abstract

We consider subdivisions of a convex body G in two subsets E and G∖E. 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.