Sharp estimates of the Kobayashi metric and Gromov hyperbolicity

Abstract

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.

26 pages, 3 figures

References in corpus (2)

• Estimates of the Kobayashi metric on almost complex manifolds
• Floer homology, symplectic and complex hyperbolicities

Cited by in corpus (2)

• Monge-Ampère operator on four dimensional almost complex manifolds
• On the Gromov hyperbolicity of the Kobayashi metric on strictly pseudoconvex regions in the almost complex case