Riemann Surface Laminations with Singularities

TL;DR

This paper introduces the fundamental concepts of holomorphic foliations and laminations, focusing on harmonic currents and ergodic properties in complex projective spaces, particularly CP^2.

Contribution

It provides foundational insights into the theory of laminations with singularities, emphasizing harmonic currents and ergodic behavior in complex settings.

Findings

Harmonic currents are central to understanding laminations.

Unique ergodicity holds for transversally Lipschitz laminations in CP^2.

Results apply to generic holomorphic foliations in complex projective spaces.

Abstract

In these introductory notes we give the basics of the theory of holomorphic foliations and laminations. The emphasis is on the theory of harmonic currents and unique ergodicity for laminations transversally Lipschitz in CP^2 and for generic holomorphic foliations in CP^2.