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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 Hermit-ian 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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https://hal.archives-ouvertes.fr/hal-01141620
Contributor : François Labourie <>
Submitted on : Monday, April 13, 2015 - 1:41:55 PM
Last modification on : Monday, October 12, 2020 - 2:28:05 PM
Long-term archiving on: : Monday, September 14, 2015 - 7:31:58 AM

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  • HAL Id : hal-01141620, version 1
  • ARXIV : 1406.4637

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François Labourie. CYCLIC SURFACES AND HITCHIN COMPONENTS IN RANK 2. 2014. ⟨hal-01141620⟩

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