Does $\mathbb{CP}^2$ admit a Riemann surface lamination structure? Every paper or article I looked at, talk only about singular laminations on $\mathbb{CP}^2$. I was wondering why. If you know something about it or you can give some reference, it would be nice.



Does $\mathbb{CP}^2$ admit a Riemann surface lamination structure?
It is conjectured that $\mathbb {CP}^2$ contains no embedded compact laminated set (without singularities) apart the smooth algebraic curves.


This is a strong form of the "Minimal Exceptional" conjecture, stating that for a singular holomorphic foliation of $\mathbb{CP}^2$, every leaf accumulates in the singular set.


Nice references about this subject are the following surveys:


* É. Ghys - *Laminations par surfaces de Riemann*. Dynamique et géométrie complexes -
Panor. Synthèses, 8, 1999.
* S. Zakeri - *Dynamics of singular holomorphic foliations on the complex projective plane*. Laminations and foliations in dynamics, geometry and topology -
Contemp. Math., 269, Amer. Math. Soc., 2001.
* J. E. Fornaess and N. Sibony - *Riemann surface laminations with singularities*. - J. Geom. Anal. 18 (2008), no. 2, 400–442.


