Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 595-605 (2004)

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Relative isodiametric inequalities

A. Cerdán, C. Miori and S. Segura Gomis

Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, E-03080-Alicante, Spain, e-mail:, e-mail:, e-mail:

Abstract: We consider subdivisions of bounded convex sets $G$ in two subsets $E$ and $G\setminus E$. We obtain several inequalities comparing the relative volume 1) with the minimum relative diameter and 2) with the maximum relative diameter. In the second case we obtain the best upper estimate only for subdivisions determined by straight lines in planar sets.

Keywords: Relative geometric inequalities, relative isodiametric inequalities, area, volume, diameter

Classification (MSC2000): 52A40, 52A10

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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

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