Abstract
In a previous paper, we showed that for all convex bodies K of constant width in \({\mathbb{R}^n, 1 \leq {\rm as}_\infty(K) \leq \frac{n+\sqrt{2n(n+1)}}{n+2}}\) , where as∞(·) denotes the Minkowski measure of asymmetry, with the equality holding on the right-hand side if K is a completion of a regular simplex, and asked whether or not the completions of regular simplices are the only bodies for the equality. A positive answer is given in this short note.
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Project supported by The NSF of Jiangsu Higher Education (08KJD110016).
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Jin, H., Guo, Q. A note on the extremal bodies of constant width for the Minkowski measure. Geom Dedicata 164, 227–229 (2013). https://doi.org/10.1007/s10711-012-9769-2
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DOI: https://doi.org/10.1007/s10711-012-9769-2