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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Aleksandrov surfaces and hyperbolicity
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by Byung-Geun Oh PDF
Trans. Amer. Math. Soc. 357 (2005), 4555-4577 Request permission

Abstract:

Aleksandrov surfaces are a generalization of two-dimensional Riemannian manifolds, and it is known that every open simply-connected Aleksandrov surface is conformally equivalent either to the unit disc (hyperbolic case) or to the plane (parabolic case). We prove a criterion for hyperbolicity of Aleksandrov surfaces which have nice tilings and where negative curvature dominates. We then apply this to generalize a result of Nevanlinna and give a partial answer for his conjecture about line complexes.
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Additional Information
  • Byung-Geun Oh
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Address at time of publication: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350
  • Email: boh@math.purdue.edu, bgoh@math.washington.edu
  • Received by editor(s): December 17, 2003
  • Published electronically: June 10, 2005
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 4555-4577
  • MSC (2000): Primary 30F20, 30D30; Secondary 28A75, 30D35
  • DOI: https://doi.org/10.1090/S0002-9947-05-03977-2
  • MathSciNet review: 2156721