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Article: Comparing the relative volume with the relative inradius and the relative width.
- Article from:
- Journal of Inequalities and Applications
- Article date:
- January 1, 2006
- Author:
CopyrightCOPYRIGHT 2006 Hindawi Publishing Corp. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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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.
1. Introduction
Let G be an open bounded convex set. Let us consider subdivisions of G in two connected subsets E and G \ E in such a way that the relative boundary ([partial derivative]E [intersection] G) is a connected topological ...