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

Journal of Inequalities and Applications volume 2006, Article number: 54542 (2006) Cite this article

Abstract

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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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Alicante, Campus de San Vicente del Raspeig, Alicante, 03080, Spain

    A. Cerdán

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  1. A. Cerdán
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Correspondence to A. Cerdán.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Cerdán, A. Comparing the relative volume with the relative inradius and the relative width. J Inequal Appl 2006, 54542 (2006). https://doi.org/10.1155/JIA/2006/54542

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  • DOI: https://doi.org/10.1155/JIA/2006/54542

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