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

2012/03/28 by Bertrand Deroin, Christophe Dupont, Deroin, Bertrand +1
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.CV #math.DS #math.GT #msc:14J29 #msc:32V40 #msc:37A50 #msc:37F75 #msc:57R30

paper · pdf · doi:10.48550/arxiv.1203.6244

29 pages

arxiv created 2012/03/28 · arxiv updated 2012/03/29

Abstract

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.

Citations

• The Geometries of 3-Manifolds

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