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.
Evolution Families and the Loewner Equation II: complex hyperbolic manifolds / Filippo Bracci; Manuel D. Contreras; Santiago Díaz-Madrigal. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 344:(2009), pp. 947-962. [10.1007/s00208-009-0340-x]
Evolution Families and the Loewner Equation II: complex hyperbolic manifolds
Filippo Bracci;
2009
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.
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