Uncountably many $C^0$ conformally distinct Lorentz surfaces and a finiteness theorem
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- by Robert W. Smyth PDF
- Proc. Amer. Math. Soc. 124 (1996), 1559-1566 Request permission
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
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- 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.
- R. Smyth and T. Weinstein, Conformally Homeomorphic Lorentz Surfaces Need Not Be Conformally Diffeomorphic, Proc. Amer. Math. Soc. 123 (1995), 3499β3506.
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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
- Received by editor(s): October 20, 1994
- Communicated by: Christopher Croke
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1559-1566
- MSC (1991): Primary 53C50, 53A30
- DOI: https://doi.org/10.1090/S0002-9939-96-03558-7
- MathSciNet review: 1346988