Geodesic
Cyclic surfaces and Hitchin components in rank 2
François Labourie1
1 Université Nice Sophia Antipolis, Laboratoire J.-A. Dieudonné, Nice, France
Annals of mathematics, Tome 185 (2017) no. 1, pp. 1-58.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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.
DOI : 10.4007/annals.2017.185.1.1

François Labourie 1

1 Université Nice Sophia Antipolis, Laboratoire J.-A. Dieudonné, Nice, France 
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François Labourie. Cyclic surfaces and Hitchin components in rank 2. Annals of mathematics, Tome 185 (2017) no. 1, pp. 1-58. doi : 10.4007/annals.2017.185.1.1. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.1.1/

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