Year: 2024
Type: article
Abstract: A translation surface is given by polygons in the plane, with sides identified by translations to create a closed Riemann surface with a flat structure away from finitely many singular points. Understanding geodesic flow on a surface involves understanding saddle connections. Saddle connections are the geodesics starting and ending at these singular points and are associated to a discrete subset of the plane. To measure the behavior of saddle connections of length at most R, we obtain precise decay rates as $$R\rightarrow \infty $$ R → ∞ for the difference in angle between two almost horizontal saddle connections.
Source: Geometriae Dedicata
Authors: Jon Chaika, Samantha Fairchild
Institutions: University of Utah, Max Planck Society
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W4403155683