Asymmetry of Convex Bodies of Constant Width |
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Authors: | HaiLin Jin Qi Guo |
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Institution: | 1.The Department of Mathematics,Suzhou University of Technology and Science,Suzhou,China |
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Abstract: | The symmetry of convex bodies of constant width is discussed in this paper. We proved that for any convex body K?? n 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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