On Bisectors in Normed Spaces
Metric Geometry
2017-07-18 v1
Abstract
In this note, we completely describe the shape of the bisector of two given points in a two-dimensional normed vector space. More precisely, we show that, depending on the position of two given points with respect to the shape of the unit circle, the following holds: the bisector of a non-strict pair of points consists of two cones and a curve, which has properties similar to those of bisectors of strict pairs of points.
Keywords
Cite
@article{arxiv.1409.1833,
title = {On Bisectors in Normed Spaces},
author = {Thomas Jahn and Margarita Spirova},
journal= {arXiv preprint arXiv:1409.1833},
year = {2017}
}
Comments
accepted for publication in Contributions to Discrete Mathematics, published by the University of Calgary