Surfaces branchées et soléno\"ıdes $\epsilon$-holomorphes

Abstract

We show that for every $\epsilon >0$, there exists a compact lamination by $\epsilon$-holomorphic surfaces in the complex projective plane, minimal, and that carries hyperbolic holonomy. We call $\epsilon$-holomorphic a real 2-dimensional surface $\Sigma$ in $\mathbf{C}{P}^2$ such that the angle between $T\Sigma$ and $iT\Sigma$ is uniformly bounded by $\epsilon$. When $\epsilon$ is sufficiently small, such surfaces are in particular symplectic.

22 pages, 9 figures