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Uniqueness of complex geodesics and characterization of circular domains

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Abstract

We study complex geodesics for complex Finsler metrics and prove a uniqueness theorem for them. The results obtained are applied to the case of the Kobayashi metric for which, under suitable hypotheses, we describe the exponential map and the relationship between the indicatrix and small geodesic balls. Finally, exploiting the connection between intrinsic metrics and the complex Monge-Ampère equation, we give characterizations for circular domains in ℂn.

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Authors and Affiliations

  1. Dipartimento di Matematica, Seconda Università di Roma, 00173, Roma, Italy

    Marco Abate & Giorgio Patrizio

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  1. Marco Abate
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  2. Giorgio Patrizio
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Abate, M., Patrizio, G. Uniqueness of complex geodesics and characterization of circular domains. Manuscripta Math 74, 277–297 (1992). https://doi.org/10.1007/BF02567672

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  • DOI: https://doi.org/10.1007/BF02567672

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