Sharp estimates of the Kobayashi metric and Gromov hyperbolicity

Florian Bertrand (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Mots clés: Almost complex structure; Kobayashi metric; Gromov hyperbolic space

Domaines: Variables complexes [math.CV]

Florian Bertrand. Sharp estimates of the Kobayashi metric and Gromov hyperbolicity. 2008. ⟨hal-00201771⟩