Abstract
We give a complete and self-contained proof of a folklore theorem which says that in an Alexandrov space the distance between a point on a geodesic and a compact set is a right-differentiable function of . 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.
Citation
Logan S. Fox. Peter Oberly. J. J. P. Veerman. "One-sided derivative of distance to a compact set." Rocky Mountain J. Math. 51 (2) 491 - 508, April 2021. https://doi.org/10.1216/rmj.2021.51.491
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