Total curvature and simple pursuit on domains of curvature bounded above
Total curvature and simple pursuit on domains of curvature bounded above
复制标题
总曲率和对上面有界的曲率域的简单追求
DOI：
10.1007/s10711-010-9481-z
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发表时间：
2009
影响因子：
0.5
通讯作者：
R. Ghrist
中科院分区：
文献类型：
--
作者：
S. Alexander;R. Bishop;R. Ghrist
我们展示了曲线incat(0)和cat(K)空间（K> 0）的周半径和渐近行为如何由总曲率的增长率控制。我们将我们的结果应用于具有简单追逐运动的捕获类型的追捕和逃避游戏，推广了已知的凸欧几里得域的结果，并获得了凸欧几里得域的新结果，并且比这些更普遍。
We show how circumradius and asymptotic behavior of curves incat(0) andcat(K) spaces (K> 0) are controlled by growth rates of total curvature. We apply our results to pursuit and evasion games of capture type with simple pursuit motion, generalizing results that are known for convex Euclidean domains, and obtaining results that are new for convex Euclidean domains and hold on playing fields vastly more general than these.