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Pré-Publication, Document De Travail Année : 2009

Multi Black Holes and Earthquakes on Riemann surfaces with boundaries

Résumé

We prove an "Earthquake Theorem" for hyperbolic metrics with geodesic boundary on a compact surfaces $S$ with boundary: given two hyperbolic metrics with geodesic boundary on a surface with $k$ boundary components, there are $2^k$ right earthquakes transforming the first in the second. An alternative formulation arises by introducing the enhanced Teichmueller space of S: We prove that any two points of the latter are related by a unique right earthquake. The proof rests on the geometry of ''multi-black holes'', which are 3-dimensional anti-de Sitter manifolds, topologically the product of a surface with boundary by an interval.

Dates et versions

hal-00636432 , version 1 (27-10-2011)

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Francesco Bonsante, Kirill Krasnov, Jean-Marc Schlenker. Multi Black Holes and Earthquakes on Riemann surfaces with boundaries. 2009. ⟨hal-00636432⟩
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