Examples of Minimal Laminations and Associated Currents

TL;DR

This paper constructs examples of holomorphic minimal laminations with specific dynamical properties, including the existence of multiple singular currents and the absence of harmonic currents, and explores their embeddings into projective space.

Contribution

It provides new explicit examples of minimal laminations with unique dynamical features and analyzes their associated currents and embeddings.

Findings

Existence of minimal laminations with infinitely many mutually singular closed currents

Construction of laminations with no non-closed harmonic currents

Embeddings of laminations into projective space

Abstract

In this paper, we construct various examples of holomorphic laminations, with leaves of dimension 1, and we also study some of their dynamical properties. In particular we study existence and uniqueness of positive closed currents. We construct minimal laminations with infinitely many mutually singular closed currents and no non-closed harmonic current. We also consider embeddings to projective space.