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

Florian Bertrand (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Mots clés: Almost complex structure; peak plurisubharmonic functions; Kobayashi pseudometric; D'Angelo type

Domaines: Variables complexes [math.CV]

Florian Bertrand. Pseudoconvex regions of finite D'Angelo type in four dimensional almost complex manifolds. 2007. ⟨hal-00177647⟩