Sharp estimates of the Kobayashi metric and Gromov hyperbolicity

Details Sharp estimates of the Kobayashi metric and Gromov hyperbolicity Sharp estimates of the Kobayashi metric and Gromov hyperbolicity

2008-01-03

arxiv.org/abs/0801.0505v1

Mathematics

Complex Variables

26 pages, 3 figures

Scientific paper

Let D be a smooth relatively compact and strictly J-pseudoconvex domain in a four dimensional almost complex manifold (M,J). We give sharp estimates of the Kobayashi metric. Our approach is based on an asymptotic quantitative description of both the domain D and the almost complex structure J near a boundary point. Following Z.M.Balogh and M.Bonk, these sharp estimates provide the Gromov hyperbolicity of the domain D.

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