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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M. D. Contreras and S. Díaz-Madrigal were partially supported by the Ministerio de Ciencia e Innovación and the European Union (FEDER), project MTM2006-14449-C02-01, by La Consejería de Educación y Ciencia de la Junta de Andalucía, and by the European Science Foundation Research Networking Programme HCAA.
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Bracci, F., Contreras, M.D. & Díaz-Madrigal, S. Evolution families and the Loewner equation II: complex hyperbolic manifolds. Math. Ann. 344, 947–962 (2009). https://doi.org/10.1007/s00208-009-0340-x
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DOI: https://doi.org/10.1007/s00208-009-0340-x