Minimal sets of foliations on complex projective spaces

Riemann Surface Laminations with Singularities

“…The result was first proved by Camacho, Lins-Neto, Sad [12] for holomorphic foliations in P 2 and by Hurder-Mitsumatsu in the C 1 case. [ α ]dμ(α), then T = [ β ]dμ(β).…”

Foliations on the complex projective plane with many parabolic leaves

“…If KC\ (J Sj = 0, then K corresponds to a compact minimal j=i j=i set of .^Icp^Sing^); but this is not possible because such a minimal set cannot support a holonomy invariant measure [CLS1]. Hence K intersects some sphere Si, and KnSi is a compact set saturated by the foliation Q\s,, which is a one -dimensional foliation with two hyperbolic closed leaves as limit set.…”

Uniformization of the leaves of a rational vector field

“…So, the transverse measure has support on the complement of the basin of attraction of the critical points. This set (the support of the measure) is a Riemann surface lamination and it is shown in [4] that there are no invariant transverse measures there.…”