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

• Autores: Bertrand Deroin
• Localización: Topology, ISSN 0040-9383, Vol. 45, Nº 3, 2006, págs. 495-512
• Idioma: inglés
• DOI: 10.1016/j.top.2005.09.001
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• Resumen

  • 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