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

2007/10/08 by Bertrand, Florian
#32Q45 #32Q60 #32Q65 #32T25 #32T40 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.0710.1605

Abstract

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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