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

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

2012-03-28

arxiv.org/abs/1203.6244v1

Mathematics

Complex Variables

29 pages

Scientific paper

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.

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