On the Gromov hyperbolicity of the Kobayashi metric on strictly pseudoconvex regions in the almost complex case

摘要

We prove that every bounded strictly J-convex region equipped with the Kobayashi metric is hyperbolic in the sense of Gromov. We give various consequences of this fact, in particular concerning the dynamics of pseudo-holomorphic maps. Keywords Kobayashi metric - Gromov hyperbolicity - Almost complex manifolds Mathematics Subject Classification (2000) 32T15 - 32Q45 - 32Q60 - 53C22