CYCLIC SURFACES AND HITCHIN COMPONENTS IN RANK 2

Abstract : We prove that given a Hitchin representation in a real split rank 2 group G 0 , there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrization of the Hitchin components by a Hermitian bundle over Teichmüller space. The proof goes through introducing holomorphic curves in a suitable bundle over the symmetric space of G 0. Some partial extensions of the construction hold for cyclic bundles in higher rank.
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Submitted on : Thursday, June 9, 2016 - 2:40:28 PM
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François Labourie. CYCLIC SURFACES AND HITCHIN COMPONENTS IN RANK 2. Annals of Mathematics, Princeton University, Department of Mathematics, 2016, 184 (2). ⟨hal-01329436⟩

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