Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
3/2005
Almost-holomorphic and totally real solenoids in complex surfaces
Bertrand Deroin
Abstract
We show that there exists a lipschitz almost-complex structure on ${\bf C}P^2$, arbitrary close to the standard one, for which there exists 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 $\delta$ in the interval $(0,\delta_{max})$, where $\delta_{max}=1.6309..$. We also show that there exists a compact lamination by totally real surfaces in ${\bf C}^2$ with the same properties. Our laminations are transversally totally disconnected, and for this reason are called solenoids.
