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On inner parallel bodies and quermassintegrals

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Abstract

Due to the “uncontrollable behavior“ of the inner parallel bodies of a convex body K ⊂ ℝn regarding its boundary structure, it is not possible to get precise formulae for their volume/quermassintegrals, contrary to the case of the outer parallel bodies. In this paper we provide (sharp) bounds for the quermassintegrals of the inner parallel bodies, studying previously some particular properties of their boundary in terms of their outer normal vectors.

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Authors and Affiliations

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

    M. A. Hernández Cifre & E. Saorín

Authors
  1. M. A. Hernández Cifre
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  2. E. Saorín
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Correspondence to M. A. Hernández Cifre.

Additional information

The first author is supported by Dirección General de Investigación (MEC) MTM2007-64504 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.

The second author is supported by Project Phenomena in High Dimension MRTNCT-2004-511953 of the European Community.

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Hernández Cifre, M.A., Saorín, E. On inner parallel bodies and quermassintegrals. Isr. J. Math. 177, 29–47 (2010). https://doi.org/10.1007/s11856-010-0037-6

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  • DOI: https://doi.org/10.1007/s11856-010-0037-6

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