Complex earthquakes and Teichmüller theory

Author:
Curtis T. McMullen

Journal:
J. Amer. Math. Soc. **11** (1998), 283-320

MSC (1991):
Primary 30F10, 30F40, 32G15

DOI:
https://doi.org/10.1090/S0894-0347-98-00259-8

MathSciNet review:
1478844

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Abstract: It is known that any two points in Teichmüller space are joined by an earthquake path. In this paper we show any earthquake path extends to a proper holomorphic mapping of a simply-connected domain into Teichmüller space, where . These complex earthquakes relate Weil-Petersson geometry, projective structures, pleated surfaces and quasifuchsian groups. Using complex earthquakes, we prove grafting is a homeomorphism for all 1-dimensional Teichmüller spaces, and we construct bending coordinates on Bers slices and their generalizations. In the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold.

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Additional Information

DOI:
https://doi.org/10.1090/S0894-0347-98-00259-8

Received by editor(s):
March 8, 1996

Received by editor(s) in revised form:
October 21, 1997

Additional Notes:
The author’s research was partially supported by the NSF

Article copyright:
© Copyright 1998
American Mathematical Society