Conformal Mappings from the Upper Half Plane to Fundamental Domains on the Hyperbolic Plane

Mark Harmer, Gaven Martin

Abstract

We use the classical theory of Schwarz-Christoffel mappings to find conformal maps from the upper half plane to triangular regions in the hyperbolic plane. We then find the pullback of the (hyperbolic) Laplace-Beltrami operator to the upper half plane.

Keywords
hyperbolic geometry, Schwarz-Christoffel maps

Math Review Classification

Last Updated
23 June 2003

Length
7 pages

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