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Evolution families and the Loewner equation II: complex hyperbolic manifolds

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133, Rome, Italy

    Filippo Bracci

  2. Camino de los Descubrimientos, s/n, Departamento de Matemática Aplicada II, Escuela Técnica Superior de Ingenieros, Universidad de Sevilla, 41092, Sevilla, Spain

    Manuel D. Contreras & Santiago Díaz-Madrigal

Authors
  1. Filippo Bracci
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  2. Manuel D. Contreras
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  3. Santiago Díaz-Madrigal
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Correspondence to Filippo Bracci.

Additional information

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

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