Resumen de Examples of almost-holomorphic and totally real laminations in complex surfaces

Bertrand Deroin

• We show that there exists a Lipschitz almost-complex structure J on CP2, arbitrarily close to the standard one, and a compact lamination by J-holomorphic curves satisfying the following properties: it is minimal, it has hyperbolic holonomy and it is transversally Lipschitz. Its transverse Hausdorff dimension can be any number d in an interval (0,dmax) where . We also show that there is a compact lamination by totally real surfaces in C2 with the same properties, unless the transverse dimension can be any number 0