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A characterization of theMM*-position of a convex body in terms of covariance matrices

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Abstract

We characterize the position of a convex bodyK such that it minimizesM(TK)M*(TK) (theMM*-position) in terms of properties of the measures ‖ · ‖ K d σ(·) and ‖ · ‖ K °d σ(·), answering a question posed by A. Giannopoulos and V. Milman. The techniques used allow us to study other extremal problems in the context of dual Brunn-Minkowski theory.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Zaragoza, Ciudad Universitaria s/n, 50009, Zaragoza, Spain

    Jesús Bastero & Miguel Romance

Authors
  1. Jesús Bastero
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  2. Miguel Romance
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Correspondence to Jesús Bastero.

Additional information

Partially supported by MCYT Grant (Spain) BFM2001-1793 and FEDER funds from UE.

Partially supported by MCYT Grant (Spain) BFM2001-1793 and FEDER funds from UE.

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Bastero, J., Romance, M. A characterization of theMM*-position of a convex body in terms of covariance matrices. Isr. J. Math. 141, 145–156 (2004). https://doi.org/10.1007/BF02772216

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  • DOI: https://doi.org/10.1007/BF02772216

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