Some invariant properties of quasi-M\"obius maps
Metric Geometry
2017-07-06 v4
Abstract
We investigate properties which remain invariant under the action of quasi-M\"obius maps of quasi-metric spaces. A metric space is called doubling with constant D if every ball of finite radius can be covered by at most D balls of half the radius. It is shown that the doubling property is an invariant property for (quasi-)M\"obius spaces. Additionally it is shown that the property of uniform disconnectedness is an invariant for (quasi-)M\"obius spaces as well.
Keywords
Cite
@article{arxiv.1603.07521,
title = {Some invariant properties of quasi-M\"obius maps},
author = {Loreno Heer},
journal= {arXiv preprint arXiv:1603.07521},
year = {2017}
}
Comments
14 pages, extends the previous version with applications of the theorems