Infinitesimal generators and the Loewner equation on complete hyperbolic manifolds

Abstract

We characterize infinitesimal generators on complete hyperbolic complex manifolds without any regularity assumption on the Kobayashi distance. This allows to prove a general Loewner type equation with regularity of any order $d\in [1,+\infty ]$. Finally, based on these results, we focus on some open problems naturally arising.

13 pages; misprints corrected and some proofs clarified

References in corpus (2)

• Evolution Families and the Loewner Equation I: The Unit Disc
• Holomorphic evolution: metamorphosis of the Loewner equation