Real and complex earthquakes
Real and complex earthquakes
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真实且复杂的地震
DOI：
10.1090/s0002-9947-05-03651-2
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发表时间：
2005
影响因子：
1.3
通讯作者：
D. Šarić
中科院分区：
文献类型：
--
作者：
D. Šarić
我们考虑（真实的）地震，并通过它们的扩展，双曲平面H2的复杂地震。我们证明了限制在H2的边界S1上的地震是拟对称映射当且仅当它的地震测度是有界的。将一个地震测度与一个正参数相乘，得到一条地震路径，因此，具有有界测度的地震路径是泛Teichmiiller空间中的一条路径。本文将有界地震的真实的参数推广到虚部较小的复参数。这样得到的复地震（或弯曲）在参数上是全纯的。此外，小虚部复参数弯曲对S1的限制是S1在复平面上的全纯运动。特别地，具有有界地震测度的真实的地震路径的参数是解析的。
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.