Cyclic surfaces and Hitchin components in rank 2

François Labourie

doi:https://doi.org/10.4007/annals.2017.185.1.1

Abstract

We prove that given a Hitchin representation in a split real rank 2 group $\mathsf{G}_0$, there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrisation of the Hitchin component by a Hermitian bundle over Teichmüller space. The proof goes through introducing holomorphic curves in a suitable bundle over the symmetric space of $\mathsf{G}_0$. Some partial extensions of the construction hold for cyclic bundles in higher rank.

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Cyclic surfaces and Hitchin components in rank 2

Abstract

Authors