Pseudoconvex regions of finite D'Angelo type in four dimensional almost complex manifolds

Details Pseudoconvex regions of finite D'Angelo type in four dimensional almost complex manifolds Pseudoconvex regions of finite D'Angelo type in four dimensional almost complex manifolds

2007-10-08

arxiv.org/abs/0710.1605v1

Mathematics

Complex Variables

34 pages

Scientific paper

Let D be a J-pseudoconvex region in a smooth almost complex manifold (M,J) of real dimension four. We construct a local peak J-plurisubharmonic function at every boundary point p of finite D'Angelo type. As applications we give local estimates of the Kobayashi pseudometric, implying the local Kobayashi hyperbolicity of D at p. In case the point p is of D'Angelo type less than or equal to four, or the approach is nontangential, we provide sharp estimates of the Kobayashi pseudometric.

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