Abstract
Let \(\mathcal{X}\) be a Euclidean space of dimension n. Recall that \(\mathfrak{B} = \mathfrak{B}_{\mathcal{X}}\) denotes the space of all convex bodies in \(\mathcal{X}\) equipped with the Hausdorff metric d H . In Section 1.4, in an application of Helly’s theorem, we briefly encountered the concept of distortion ratio (Corollary 1.4.2). In the present section we will make a more elaborate analysis of this concept. Throughout, \(\mathcal{C}\in \mathfrak{B}\) will denote a convex body in \(\mathcal{X}\). The distortion ratio can be defined with respect to interior and exterior points of \(\mathcal{C}\). We split our treatment accordingly.
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Toth, G. (2015). Affine Diameters and the Critical Set. In: Measures of Symmetry for Convex Sets and Stability. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-23733-6_2
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