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

Abstract

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