Abstract
The symmetry of convex bodies of constant width is discussed in this paper. We proved that for any convex body K⊂ℝn of constant width, \(1\leq \mathrm{as}_{\infty}(K)\leq\frac{n+\sqrt{2n(n+1)}}{n+2}\), where as∞(⋅) denotes the Minkowski measure of asymmetry for convex bodies. Moreover, the equality holds on the left-hand side precisely iff K is an Euclidean ball and the upper bounds are attainable, in particular, if n=3, the equality holds on the right-hand side if K is a Meissner body.
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Jin, H., Guo, Q. Asymmetry of Convex Bodies of Constant Width. Discrete Comput Geom 47, 415–423 (2012). https://doi.org/10.1007/s00454-011-9370-8
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DOI: https://doi.org/10.1007/s00454-011-9370-8