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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Completing the conformal boundary of a simply connected Lorentz surface


Author: Robert W. Smyth
Journal: Proc. Amer. Math. Soc. 130 (2002), 841-847
MSC (2000): Primary 53C50, 53A30
Published electronically: August 29, 2001
MathSciNet review: 1866040
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Abstract: This paper extends Kulkarni's conformal boundary $\partial{\mathcal{L}}$ for a simply connected Lorentz surface $\mathcal{L}$ to a compact conformal boundary $\partial^c\mathcal{L}$. The procedure used is analogous to Carathéodory's construction (in the definite metric setting) of prime ends from the accessible points of a bounded simply connected planar domain. The space $\partial^c\mathcal{L}$ of conformal boundary elements is homeomorphic to the circle, and contains Kulkarni's conformal boundary $\partial{\mathcal{L}}$ as a dense subspace.


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Additional Information

Robert W. Smyth
Affiliation: Department of Natural Science, Mathematics and Computer Science, Georgian Court College, Lakewood, New Jersey 08701
Email: smythr@georgian.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06067-1
PII: S 0002-9939(01)06067-1
Keywords: Indefinite metric, conformal geometry, foliation theory
Received by editor(s): April 17, 2000
Received by editor(s) in revised form: September 5, 2000
Published electronically: August 29, 2001
Communicated by: Wolfgang Ziller
Article copyright: © Copyright 2001 American Mathematical Society