Estimates of the Kobayashi metric on almost complex manifolds

Hervé Gaussier (1) , Alexandre Sukhov (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We establish a lower estimate for the Kobayashi-Royden infinitesimalpseudometric on an almost complex manifold $(M,J)$ admitting a boundedstrictly plurisubharmonic function. We apply this result to study theboundary behaviour of the metric on a strictly pseudoconvex domain in$M$ and to give a sufficient condition for the complete hyperbolicityof a domain in $(M,J)$. Finally we obtain the regularity up to thebounday of $J$-holomorphic discs attached to a totally realsubmanifold in $M$.

Domaines: Variables complexes [math.CV]; Géométrie différentielle [math.DG]

Hervé Gaussier, Alexandre Sukhov. Estimates of the Kobayashi metric on almost complex manifolds. 2004. ⟨hal-00000525v2⟩