Published In

Rocky Mountain Journal of Mathematics

Document Type

Post-Print

Publication Date

4-1-2021

Subjects

Boundary value problems

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 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.

Rights

Rights: Copyright © 2021 Rocky Mountain Mathematics Consortium

Description

This is the author's accepted manuscript of an article that was accepted for publication in the Rocky Mountain Journal of Mathematic. A definitive version was subsequently published as: One-sided derivative of distance to a compact set. Rocky Mountain Journal of Mathematics,51(2). https://doi.org/10.1216/rmj.2021.51.491

DOI

10.1216/rmj.2021.51.491

Persistent Identifier

https://archives.pdx.edu/ds/psu/36142

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