Entropy for hyperbolic Riemann surface laminations II

TL;DR

This paper investigates the hyperbolic entropy of Brody hyperbolic Riemann surface foliations with isolated singularities on compact complex surfaces, establishing its finiteness and providing continuity estimates for the Poincare metric.

Contribution

It proves the finiteness of hyperbolic entropy for such foliations and extends continuity estimates of the Poincare metric to higher-dimensional manifolds.

Findings

Hyperbolic entropy is finite for Brody hyperbolic foliations with isolated singularities.

Provides estimates on the modulus of continuity of the Poincare metric on leaves.

Extends results to foliations on higher-dimensional manifolds.

Abstract

Consider a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated singularities on a compact complex surface. We show that its hyperbolic entropy is finite. We also estimate the modulus of continuity of the Poincare metric on leaves. The estimate holds for foliations on manifolds of higher dimension.