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- W4230485628 abstract "A Lorentz surface $mathcal {L}$ is an ordered pair (S, [h]) where S is an oriented ${C^infty }$ 2-manifold and [h] the set of all ${C^infty }$ metrics conformally equivalent to a fixed ${C^infty }$ Lorentzian metric h on S. (Thus Lorentz surfaces are the indefinite metric analogs of Riemann surfaces.) This paper describes subsets of the Minkowski 2-plane which are conformally homeomorphic, but not even ${C^1}$ conformally diffeomorphic. It also describes subsets of the Minkowski 2-plane which are ${C^j}$ but not ${C^{j + 1}}$ conformally diffeomorphic for any fixed $j = 1,2, ldots$. Finally, the paper describes a Lorentz surface conformally homeomorphic to a subset of the Minkowski 2-plane, but not ${C^1}$ conformally diffeomorphic to any subset of the Minkowski 2-plane." @default.
- W4230485628 created "2022-05-11" @default.
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- W4230485628 date "1995-11-01" @default.
- W4230485628 modified "2023-09-26" @default.
- W4230485628 title "Conformally Homeomorphic Lorentz Surfaces need not be Conformally Diffeomorphic" @default.
- W4230485628 doi "https://doi.org/10.2307/2161098" @default.
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