Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 45, No. 2, pp. 595-605 (2004)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 595-605 (2004) |
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Relative isodiametric inequalitiesA. Cerdán, C. Miori and S. Segura GomisDepartamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, E-03080-Alicante, Spain, e-mail: aacs@alu.ua.es, e-mail: cm4@alu.ua.es, e-mail: Salvador.Segura@ua.esAbstract: 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 Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
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