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Fixed points of compositions of earthquakes

Authors
  • Bonsante, Francesco
  • Schlenker, Jean-Marc
Type
Preprint
Publication Date
Jul 09, 2010
Submission Date
Dec 18, 2008
Identifiers
arXiv ID: 0812.3471
Source
arXiv
License
Yellow
External links

Abstract

Let S be a closed surface of genus at least 2, and consider two measured geodesic laminations that fill S. Right earthquakes along these laminations are diffeomorphisms of the Teichm\"uller space of S. We prove that the composition of these earthquakes has a fixed point in the Teichm\"uller space. Another way to state this result is that it is possible to prescribe any two measured laminations that fill a surface as the upper and lower measured bending laminations of the convex core of a globally hyperbolic AdS manifold. The proof uses some estimates from the geometry of those AdS manifolds.

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