Holomorphic foliations transverse to manifolds with corners
Toshikazu Ito Bruno Scárdua
Discrete & Continuous Dynamical Systems - A 2009, 25(2): 537-544 doi: 10.3934/dcds.2009.25.537
We study the geometrical and dynamical properties of a holomorphic vector field on a complex surface, assumed to be transverse to the boundary of a domain which is a non-smooth manifold with boundary and corners. We obtain hyperbolicity and prove a compact leaf result. For a pseudoconvex domain with boundary diffeomorphic to the boundary of a bidisc in $\mathbb C^2$ the foliation is pull-back of a liner hyperbolic foliation. If moreover the diffeomorphism is transversely holomorphic then we have linearization.
keywords: Holomorphic foliation manifold with corners hyperbolic holonomy.

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