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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Complex earthquakes and Teichmüller theory
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by Curtis T. McMullen
J. Amer. Math. Soc. 11 (1998), 283-320
DOI: https://doi.org/10.1090/S0894-0347-98-00259-8

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 $\mathbb R \rightarrow T(S)$ extends to a proper holomorphic mapping of a simply-connected domain $D$ into Teichmüller space, where $\mathbb R \subset D \subset \mathbb C$. 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.
References
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Bibliographic Information
  • 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
  • © Copyright 1998 American Mathematical Society
  • 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