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Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains

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Commentarii Mathematici Helvetici

Abstract.

We give an estimate for the distance function related to the Kobayashi metric on a bounded strictly pseudoconvex domain with C 2-smooth boundary. Our formula relates the distance function on the domain with the Carnot-Carathéodory metric on the boundary. The estimate is precise up to a bounded additive term. As a corollary we conclude that the domain equipped with this distance function is hyperbolic in the sense of Gromov.

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Authors and Affiliations

  1. Universität Bern, Mathematisches Institut, Sidlerstr. 5, CH-3012 Bern, Switzerland, e-mail: zoltan@math-stat.unibe.ch, , , , , , CH

    Z. M. Balogh

  2. Institut für Analysis, Tech. Univ. Braunschweig, D-38106 Braunschweig, Germany, e-mail: M.Bonk@tu-bs.de, , , , , , DE

    M. Bonk

Authors
  1. Z. M. Balogh
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  2. M. Bonk
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Received: January 11, 2000.

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Balogh, Z., Bonk, M. Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains. Comment. Math. Helv. 75, 504–533 (2000). https://doi.org/10.1007/s000140050138

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  • DOI: https://doi.org/10.1007/s000140050138

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