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Minimal surfaces and symplectic structures of moduli spaces

Abstract : Given a closed surface S of genus at least 2, we compare the symplectic structure of Taubes' moduli space of minimal hyperbolic germs with the Goldman sym-plectic structure on the character variety X (S, P SL(2, C)) and the affine cotangent symplectic structure on the space of complex projective structures CP(S) given by the Schwarzian parametrization. This is done in restriction to the moduli space of almost-Fuchsian structures by involving a notion of renormalized volume, used to relate the geometry of a minimal surface in a hyperbolic 3-manifold to the geometry of its ideal conformal boundary.
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https://hal.archives-ouvertes.fr/hal-01275183
Contributor : Brice Loustau <>
Submitted on : Wednesday, February 17, 2016 - 4:29:58 AM
Last modification on : Wednesday, September 16, 2020 - 4:05:32 PM
Long-term archiving on: : Wednesday, May 18, 2016 - 1:09:38 PM

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Brice Loustau. Minimal surfaces and symplectic structures of moduli spaces. 2016. ⟨hal-01275183⟩

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