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January, 2002 The Geometry of Finite Topology Bryant Surfaces Quasi-Embedded in a Hyperbolic Manifold
Laurent Hauswirth, Pedro Roitman, Harold Rosenberg
J. Differential Geom. 60(1): 55-101 (January, 2002). DOI: 10.4310/jdg/1090351084

Abstract

We prove that a finite topology properly embedded Bryant surface in a complete hyperbolic 3-manifold has finite total curvature. This permits us to describe the geometry of the ends of such a Bryant surface. Our theory applies to a larger class of Bryant surfaces, which we call quasi-embedded. We give many examples of these surfaces and we show their end structure is modelled on the quotient of a ruled Bryant catenoid end by a parabolic isometry. When the ambient hyperbolic 3-manifold is hyperbolic 3-space, the theorems we prove here were established by Collin, Hauswirth and Rosenberg, 2001.

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Laurent Hauswirth. Pedro Roitman. Harold Rosenberg. "The Geometry of Finite Topology Bryant Surfaces Quasi-Embedded in a Hyperbolic Manifold." J. Differential Geom. 60 (1) 55 - 101, January, 2002. https://doi.org/10.4310/jdg/1090351084

Information

Published: January, 2002
First available in Project Euclid: 20 July 2004

zbMATH: 1067.53044
MathSciNet: MR1924592
Digital Object Identifier: 10.4310/jdg/1090351084

Rights: Copyright © 2002 Lehigh University

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Vol.60 • No. 1 • January, 2002
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