Sharp estimates of the Kobayashi metric and Gromov hyperbolicity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:345

Article

Bertrand, Florian

关键词: almost complex structure;    Kobayashi metric;    Gromov hyperbolic space;   

DOI  :  10.1016/j.jmaa.2008.04.057

来源: Elsevier

【 摘 要 】

Let D = {rho < 0} be a smooth relatively compact domain in a four-dimensional almost complex manifold (M, J), where rho is a J-plurisubharmonic function on a neighborhood of (D) over bar and strictly J-plurisubharmonic on a neighborhood of partial derivative D. 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 [Z.M. Balogh, M. Bonk, Gromov hyperbolicity and the Kobayashi metric on strictly pseudoconvex domains, Comment. Math. Helv. 75 (2000) 504-533], these sharp estimates provide the Gromov hyperbolicity of the domain D. (c) 2008 Elsevier Inc. All rights reserved.

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