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Measures of Symmetry and Stability

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Measures of Symmetry for Convex Sets and Stability

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Abstract

In this section we give another interpretation of the Minkowski measure of a convex body (Section 2.1) in terms of supporting hyperplanes. We show that the associated “support ratio” corresponds to our earlier distortion ratio through the concept of duality (or polarity) between convex bodies. We introduce and discuss duality by means of “musical correspondences” which prove to be transparent and convenient technical tools to derive various simple facts such as the so-called Bipolar Theorem.

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  1. Department of Mathematical Sciences, Rutgers University, Camden, NJ, USA

    Gabor Toth

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  1. Gabor Toth
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Toth, G. (2015). Measures of Symmetry and Stability. In: Measures of Symmetry for Convex Sets and Stability. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-23733-6_3

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