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- W1847899470 abstract "We consider (real) earthquakes and, by their extensions, complex earthquakes of the hyperbolic plane H 2 . We show that an earthquake restricted to the boundary S 1 of H 2 is a quasisymmetric map if and only if its earthquake measure is bounded. Multiplying an earthquake measure by a positive parameter we obtain an earthquake path. Consequently, an earthquake path with a bounded measure is a path in the universal Teichmiiller space. We extend the real parameter for a bounded earthquake into the complex parameter with small imaginary part. Such obtained complex earthquake (or bending) is holomorphic in the parameter. Moreover, the restrictions to S 1 of a bending with complex parameter of small imaginary part is a holomorphic motion of S 1 in the complex plane. In particular, a real earthquake path with bounded earthquake measure is analytic in its parameter." @default.
- W1847899470 created "2016-06-24" @default.
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- W1847899470 date "2005-02-04" @default.
- W1847899470 modified "2023-09-26" @default.
- W1847899470 title "Real and complex earthquakes" @default.
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- W1847899470 doi "https://doi.org/10.1090/s0002-9947-05-03651-2" @default.
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