Geodesic Triangles in H² with Short Sides

Authors

Rita Gitik Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, United States https://orcid.org/0000-0003-2874-1911

DOI:

https://doi.org/10.37256/cm.3420221362

Keywords:

hyperbolic surface, Poincaré disc, geodesic, covering space, tree, free group

Abstract

We prove that if M is an orientable hyperbolic surface without boundary (possibly compact, possibly with infinitely generated fundamental group) and γ is a closed geodesic in M then any side of any triangle formed by distinct lifts of γ in H² is shorter than γ.

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Published

2022-10-17

Issue

Contemporary Mathematics, Volume 3 Issue 4 (2022), 386-561

Section

Research Article