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On The (Dual) Blaschke Diagram

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Abstract

In this paper we study the behavior of the roots of the Steiner polynomial of a convex body when we embed it in a higher dimensional space. In the 3-dimensional case, the involved sets will follow a precise pattern when they are mapped into the Blaschke diagram. We also construct and characterize the so-called dual Blaschke diagram. As an immediate consequence of it we will get a new characterization of dual quermassintegrals in dimension \(n=3\).

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Acknowledgements

The authors would like to strongly thank the anonymous referee for the very valuable comments and helpful suggestions; his/her observations allowed us to considerably improve the article.

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Authors and Affiliations

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

    María A. Hernández Cifre & Miriam Tárraga

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  1. María A. Hernández Cifre
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  2. Miriam Tárraga
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Correspondence to María A. Hernández Cifre.

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Supported by: MICINN/FEDER project PGC2018-097046-B-I00; “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, 19901/GERM/15.

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Hernández Cifre, M.A., Tárraga, M. On The (Dual) Blaschke Diagram. Bull Braz Math Soc, New Series 52, 291–305 (2021). https://doi.org/10.1007/s00574-020-00204-x

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  • DOI: https://doi.org/10.1007/s00574-020-00204-x

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