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


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.



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Correspondence to A. Cerdán.

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Cerdán, A. Comparing the relative volume with the relative inradius and the relative width. J Inequal Appl 2006, 54542 (2006).

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  • Relative Volume
  • Convex Body
  • Lower Estimate
  • Relative Width
  • General Hypersurface