Classification AMS 2010: Primary: 37A35, 37A30, 57R30; Secondary: 58J35, 58J65, 60J65.

Contents
1. Introduction
2. Basic Results
3. Regularity of the Leafwise Poincaré Metric
4. Mass-Distribution of Directed Positive Harmonic Currents
7. Lyapunov Theory for Hyperbolic Riemann Surface Laminations