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The role of the kernel in Bonnesen-style inradius inequalities

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Abstract

Sharp bounds for the volume of a convex body are obtained in terms of its surface area and other quermassintegrals. These bounds are consequences of, on the one hand, inequalities for inner parallel bodies involving mixed volumes and, on the other hand, inequalities which relate a convex body to its inner parallel bodies, its kernel and its form body.

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Acknowledgments

The author would like to thank M. A. Hernández Cifre for enlightening discussions.

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Authors and Affiliations

  1. Institut für Algebra und Geometrie, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106 , Magdeburg, Germany

    E. Saorín Gómez

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  1. E. Saorín Gómez
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Correspondence to E. Saorín Gómez.

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Communicated by A. Constantin.

Author is supported by Dirección General de Investigación MTM2011-25377 and by “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, Agencia de Ciencia y Tecnología de la Región de Murcia (Plan Regional de Ciencia y Tecnología 2007/2010), 04540/GERM/06.

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Gómez, E.S. The role of the kernel in Bonnesen-style inradius inequalities. Monatsh Math 171, 65–75 (2013). https://doi.org/10.1007/s00605-012-0431-8

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  • DOI: https://doi.org/10.1007/s00605-012-0431-8

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