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Infinitesimal generators and the Loewner equation on complete hyperbolic manifolds

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Abstract

We characterize infinitesimal generators on complete hyperbolic complex manifolds without any regularity assumption on the Kobayashi distance. This allows to prove a general Loewner type equation with regularity of any order \({d \in [1, +\infty]}\) . Finally, based on these results, we focus on some open problems naturally arising.

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Authors and Affiliations

  1. Istituto Nazionale di Alta Matematica “Francesco Severi”, Città Universitaria, Piazzale Aldo Moro 5, 00185, Rome, Italy

    Leandro Arosio

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

    Filippo Bracci

Authors
  1. Leandro Arosio
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  2. Filippo Bracci
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Correspondence to Filippo Bracci.

Additional information

L. Arosio: Titolare di una Borsa della Fondazione Roma—Terzo Settore bandita dall’Istituto Nazionale di Alta Matematica.

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Arosio, L., Bracci, F. Infinitesimal generators and the Loewner equation on complete hyperbolic manifolds. Anal.Math.Phys. 1, 337–350 (2011). https://doi.org/10.1007/s13324-011-0020-3

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  • DOI: https://doi.org/10.1007/s13324-011-0020-3

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