Hyperbolic Spaces and Ptolemy Moebius Structures
Renlong Miao, Viktor Schroeder
TL;DR
This paper characterizes Gromov hyperbolic spaces with boundaries that admit canonical Möbius structures, linking hyperbolic geometry with Möbius geometry at infinity.
Contribution
It provides a characterization of hyperbolic spaces based on the Möbius structures on their boundaries, connecting boundary geometry with the hyperbolic space itself.
Findings
Identification of conditions for boundary Möbius structures
Link between hyperbolic spaces and Ptolemy Möbius structures
Framework for analyzing hyperbolic spaces via boundary geometry
Abstract
We characterize the class of Gromov hyperbolic spaces, whose boundary at infinity allow canonical M\"obius structures.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematics and Applications · Finite Group Theory Research