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Successive radii and Minkowski addition

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Abstract

In this paper we study the behavior of the so called successive inner and outer radii with respect to the Minkowski addition of convex bodies, generalizing the well-known cases of the diameter, minimal width, circumradius and inradius. We get all possible upper and lower bounds for the radii of the sum of two convex bodies in terms of the sum of the corresponding radii.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Murcia, Spain

    Bernardo González & María A. Hernández Cifre

Authors
  1. Bernardo González
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  2. María A. Hernández Cifre
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Correspondence to María A. Hernández Cifre.

Additional information

Authors are supported by MCI, MTM2009-10418, 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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González, B., Hernández Cifre, M.A. Successive radii and Minkowski addition. Monatsh Math 166, 395–409 (2012). https://doi.org/10.1007/s00605-010-0268-y

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  • DOI: https://doi.org/10.1007/s00605-010-0268-y

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