Estimates of the Kobayashi metric on almost complex manifolds

Abstract

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M,J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in $M$ and to give a sufficient condition for the complete hyperbolicity of a domain in $(M,J)$. Finally we obtain the regularity up to the bounday of $J$-holomorphic discs attached to a totally real submanifold in $M$.

date de redaction: 2003-4-3

Cited by in corpus (3)

• Floer homology, symplectic and complex hyperbolicities
• Wong-Rosay Theorem in almost complex manifolds
• Hyperbolic distance to submanifolds in an almost-complex manifold