论文标题
与紧凑型组的距离的单侧导数
One-Sided Derivative of Distance to a Compact Set
论文作者
论文摘要
我们给出了一个民俗定理的完整且独立的证据，该证明说，在亚历山德罗夫的空间中，地球$γ$上的点$γ（t）$与紧凑型套装$ k $之间的距离是$ t $的合理函数。此外，该右衍生的值是由地理位置和任何最短路径之间的最小角度的负余弦给出的（定理4.3）。我们的处理是公制几何学的一般介绍，仅依靠基本元素，例如比较三角形和上角。
We give a complete and self-contained proof of a folklore theorem which says that in an Alexandrov space the distance between a point $γ(t)$ on a geodesic $γ$ and a compact set $K$ is a right-differentiable function of $t$. Moreover, the value of this right-derivative is given by the negative cosine of the minimal angle between the geodesic and any shortest path to the compact set (Theorem 4.3). Our treatment serves as a general introduction to metric geometry and relies only on the basic elements, such as comparison triangles and upper angles.
