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 $\varphi$ of a closed complex manifold $X$, some power ${\varphi }^k$ ($k>0$) fixes a measured Riemann surface lamination in $X$.

arXiv commentError in the proof of the main theorem. The error can not be fixed

References in corpus (1)

• Compactness theorems for the spaces of distance measure spaces and Riemann surface laminations