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Article Dans Une Revue Journal of the American Mathematical Society Année : 2016

Topology and dynamics of Levi-flats in surfaces of general type

Résumé

We focus on the topology and dynamics of minimal sets and Levi-flats in surfaces of general type. Our method relies on the ergodic theory of Riemann surfaces laminations: we use harmonic measures and Lyapunov exponents. Our first result establishes that minimal sets have large Hausdorff dimension when a leaf is simply connected. Our second result shows that the class of Anosov Levi-flats does not occur in surfaces of general type. In particular, by using rigidity results, we obtain that Levi-flats are not virtually diffeomorphic to unitary tangent bundles of hyperbolic compact surfaces, nor to hyperbolic torus bundles.

Dates et versions

hal-01346564 , version 1 (19-07-2016)

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Bertrand Deroin, Christophe Dupont. Topology and dynamics of Levi-flats in surfaces of general type. Journal of the American Mathematical Society, 2016, 29 (2), pp.495-535. ⟨10.1090/jams832⟩. ⟨hal-01346564⟩
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