Poincaré metric of holomorphic foliations with non-degenerate singularities

Abstract

Consider a Brody hyperbolic foliation $\mathcal{F}$ with non-degenerate singularities on a compact complex manifold. We show that its leafwise Poincaré metric is transversally Hölder continuous with a logarithmic slope towards the singular set of $\mathcal{F}$.

19 pages, 2 figures

References in corpus (1)

• Ergodic theorems for laminations and foliations: recent results and perspectives

Cited by in corpus (2)

• Heat diffusions on holomorphic foliations with non-degenerate singularities
• Hyperbolic entropy for harmonic measures on singular holomorphic foliations