A Compactness Theorem for Embedded Measured Riemann Surface Laminations

Abstract

We prove a compactness theorem for embedded measured hyperbolic Riemann surface laminations in a compact almost complex manifold $(X, J)$. To prove compactness result, we show that there is a suitable topology on the space of measured Riemann surface laminations induced by Levy-Prokhorov metric. As an application of the compactness theorem, we show that given a biholomorphism of $φ$ of a closed complex manifold $X$, some power $φ^k$