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
Locate the Document
DOI
10.1216/rmj.2021.51.491
Persistent Identifier
https://archives.pdx.edu/ds/psu/36142
Citation Details
Fox, Logan S.; Oberly, Peter; and Veerman, J. J. P., "One-Sided Derivative of Distance to a Compact Set" (2021). Mathematics and Statistics Faculty Publications and Presentations. 328.
https://archives.pdx.edu/ds/psu/36142
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 in Journal of Mathematics,51(2).