Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Completing the conformal boundary of a simply connected Lorentz surface

Author(s): Robert W. Smyth
Journal: Proc. Amer. Math. Soc. 130 (2002), 841-847.
MSC (2000): Primary 53C50, 53A30
Posted: August 29, 2001
MathSciNet review: 1866040
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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.

References:

1.: C. Carathéodory, Über die Begrenzung einfach zusammenhängender Gebiete, Math. Ann. 73 (1913), 323-370.
2.: G. M. Goluzin, Geometric Theory of Functions of a Complex Variable, Vol. 26: Translations of Mathematical Monographs, AMS, 1969. MR 40:308
3.: H. Hamburger, Über Kurvennetze mit isolierten Singularitäten auf geschlossen Flächen, Math. Z. 19 (1924), 50-66.
4.: N. Klarreich, Smoothability of the conformal boundary of a Lorentz surface implies `global smoothability', to appear in Geometriae Dedicata.
5.: R. Kulkarni, An analogue of the Riemann mapping theorem for Lorentz metrics, Proc. R. Soc. Lond. A 401 (1985), 117-130. MR 87e:53108
6.: F. Luo and R. Stong, An analogue of the Riemann mapping theorem for Lorentz metrics: Topological embedding of a twice foliated disc into the plane, Math Ann 309 (1997), 359-373.
7.: A. Markushevich, Theory of Functions of a Complex Variable, Chelsea, 1985. MR 56:3258
8.: R. Smyth and T. Weinstein, Conformally homeomorphic Lorentz surfaces need not be conformally diffeomorphic, Proc. Amer. Math. Soc. 123 (1995), 3499-3506. MR 96a:53083
9.: R. Smyth and T. Weinstein, How many Lorentz surfaces are there?, Topics in Geometry: In memory of Joseph D'Atri, S. Gindikin, ed., Birkhauser Verlag, 1996. MR 97c:53107
10.: R. Smyth, Uncountably many conformally distinct Lorentz surfaces and a finiteness theorem, Proc. Amer. Math. Soc. 124 (1996), 1559-1566. MR 96g:53098
11.: R. Smyth, Characterization of Lorentz surfaces via the conformal boundary, Ph.D. Thesis, Rutgers University, 1995.
12.: T. Weinstein, An Introduction to Lorentz Surfaces, de Gruyter, 1996. MR 98a:53104

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C50, 53A30

Retrieve articles in all Journals with MSC (2000): 53C50, 53A30

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: 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
Posted: August 29, 2001
Communicated by: Wolfgang Ziller
Copyright of article: Copyright 2001, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|