Mathematische Annalen

, Volume 344, Issue 4, pp 947–962 | Cite as

Evolution families and the Loewner equation II: complex hyperbolic manifolds

  • Filippo Bracci
  • Manuel D. Contreras
  • Santiago Díaz-Madrigal
Article

Abstract

We prove that evolution families on complex complete hyperbolic manifolds are in one to one correspondence with certain semicomplete non-autonomous holomorphic vector fields, providing the solution to a very general Loewner type differential equation on manifolds.

Mathematics Subject Classification (2000)

Primary 34M45 Secondary 32Q45 32W99 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Filippo Bracci
    • 1
  • Manuel D. Contreras
    • 2
  • Santiago Díaz-Madrigal
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomeItaly
  2. 2.Camino de los Descubrimientos, s/n, Departamento de Matemática Aplicada II, Escuela Técnica Superior de IngenierosUniversidad de SevillaSevillaSpain

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