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.
François Labourie. CYCLIC SURFACES AND HITCHIN COMPONENTS IN RANK 2. Annals of Mathematics, Princeton University, Department of Mathematics, 2016, 184 (2). ⟨hal-01329436⟩
