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

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uncountably many $C^0$ conformally distinct Lorentz surfaces and a finiteness theorem


Author: Robert W. Smyth
Journal: Proc. Amer. Math. Soc. 124 (1996), 1559-1566
MSC (1991): Primary 53C50, 53A30
MathSciNet review: 1346988
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper describes an uncountable family of Lorentz surfaces realized as rectangular regions in the Minkowski 2-plane $E^2_1$. A simple $C^0$ conformal invariant is defined which assigns a different real value to each Lorentz surface in the family. While these surfaces provide uncountably many $C^0$ conformally distinct, bounded, convex subsets of $E^2_1$ which are each symmetric about a properly embedded timelike curve and about a properly embedded spacelike curve, it is shown that there are only 21 $C^0$ conformally distinct, bounded, convex subsets of $E^2_1$ which are symmetric about some null line.


References [Enhancements On Off] (What's this?)

  • 1. R. S. Kulkarni, An analogue of the Riemann mapping theorem for Lorentz metrics, Proc. Roy. Soc. London Ser. A 401 (1985), no. 1820, 117–130. MR 807317 (87e:53108)
  • 2. 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, preprint.
  • 3. R. Smyth and T. Weinstein, Conformally Homeomorphic Lorentz Surfaces Need Not Be Conformally Diffeomorphic, Proc. Amer. Math. Soc. 123 (1995), 3499--3506. CMP 95:16
  • 4. T. Weinstein, An Introduction to Lorentz Surfaces, DeGruyter Expositions in Math. (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 53C50, 53A30

Retrieve articles in all journals with MSC (1991): 53C50, 53A30


Additional Information

Robert W. Smyth
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
Address at time of publication: Department of Mathematics, Georgian Court College, Lakewood, New Jersey 08701
Email: rsmyth@math.rutgers.edu, rsmyth@georgian.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03558-7
PII: S 0002-9939(96)03558-7
Keywords: Indefinite metric, conformal geometry
Received by editor(s): October 20, 1994
Communicated by: Christopher Croke
Article copyright: © Copyright 1996 American Mathematical Society