The Longest Shortest Fence and Sharp Poincaré–Sobolev Inequalities
The Longest Shortest Fence and Sharp Poincaré–Sobolev Inequalities
复制标题
最长最短栅栏和尖锐庞加莱-索博列夫不等式
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
C. Trombetti
中科院分区：
文献类型：
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作者：
L. Esposito;V. Ferone;B. Kawohl;C. Nitsch;C. Trombetti
我们证明了一个长期存在的猜想有关的击剑问题在平面上：在给定面积的平面凸集，光盘，只有光盘，最大化的最短的面积平分曲线的长度。虽然它可能看起来很直观，但结果绝不是微不足道的，因为我们还证明了在给定面积的平面凸集中，最短平分弦的长度最大化的集合是所谓的奥尔巴赫三角形。
We prove a long standing conjecture concerning the fencing problem in the plane: among planar convex sets of given area, the disc, and only the disc, maximizes the length of the shortest area-bisecting curve. Although it may look intuitive, the result is by no means trivial since we also prove that among planar convex sets of given area the set which maximizes the length of the shortest bisecting chords is the so-called Auerbach triangle.