Points joined by three shortest paths on convex surfaces
Points joined by three shortest paths on convex surfaces
复制标题
凸面上由三个最短路径连接的点
DOI：
10.1090/s0002-9939-1995-1273530-9
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
T. Zamfirescu
中科院分区：
文献类型：
--
作者：
T. Zamfirescu
设S是凸曲面，xeS.本文证明了S中与x至少有三条最短路相连的所有点的集合在S中是稠密的。它被证明，事实上，在Baire范畴的意义下，大多数凸曲面都有这个性质，对任何x。此外，在大多数凸曲面上，对于它们的大多数点，只有一个最远的点（在内在度量中），正好有三条最短路径通向那个点。
Let S be a convex surface and x e S . It is shown here that the set of all points of S joined with x by at least three shortest paths can be dense in S. It is proven that, in fact, in the sense of Baire categories most convex surfaces have this property, for any x . Moreover, on most convex surfaces, for most of their points, there is just one farthest point (in the intrinsic metric), and precisely three shortest paths lead to that point.