A note on the extremal bodies of constant width for the Minkowski measure
A note on the extremal bodies of constant width for the Minkowski measure
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DOI：
10.1007/s10711-012-9769-2
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发表时间：
2013-06
影响因子：
0.5
通讯作者：
HaiLin Jin;Qi Guo
中科院分区：
文献类型：
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作者：
HaiLin Jin;Qi Guo
在之前的论文中，我们证明了对于所有宽度恒定的凸体K，其中as∞(·)表示不对称性的明可夫斯基测度，如果K是正则单纯形的完备性，则等式在右侧成立，并询问正则单纯形的完备性是否是唯一的等式体。这篇简短的笔记给出了肯定的答案。
In a previous paper, we showed that for all convex bodiesKof constant width in, where as∞(·) denotes the Minkowski measure of asymmetry, with the equality holding on the right-hand side ifKis 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.