Minimal surfaces and symplectic structures of moduli spaces

Geometriae Dedicata - Tập 175 - Trang 309-322 - 2015
Brice Loustau1
1Département de mathématiques d’Orsay, Bâtiment 425, Université Paris-Sud, Orsay Cedex, France

Tóm tắt

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 symplectic structure on the character variety $${\fancyscript{X}}(S, { PSL}(2,{\mathbb {C}}))$$ and the affine cotangent symplectic structure on the space of complex projective structures $${\fancyscript{CP}}(S)$$ 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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Geometriae Dedicata

Tập 175

309-322

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