Evolution families and the Loewner equation II: complex hyperbolic manifolds |
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Authors: | Filippo Bracci Manuel D. Contreras Santiago Díaz-Madrigal |
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Affiliation: | (1) Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Rome, Italy;(2) Camino de los Descubrimientos, s/n, Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingenieros, Universidad de Sevilla, 41092 Sevilla, Spain |
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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. 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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Keywords: | KeywordHeading" >Mathematics Subject Classification (2000) Primary 34M45 Secondary 32Q45 32W99 |
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