Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains | Zendy

Zoltán M. Balogh | Zendy; Mario Bonk | Zendy

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Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains

Author(s) -

Zoltán M. Balogh,

Mario Bonk

Publication year - 2000

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050138

Subject(s) - mathematics , bounded function , corollary , domain (mathematical analysis) , boundary (topology) , metric (unit) , carnot cycle , pure mathematics , function (biology) , mathematical analysis , pseudoconvex function , geometry , operations management , convex optimization , physics , evolutionary biology , biology , convex combination , thermodynamics , regular polygon , economics

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-Carath eodory 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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