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
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
Copyright © 2006 A. Cerdán. 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.
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.