Estimates of the Kobayashi metric on almost complex manifolds

Details Estimates of the Kobayashi metric on almost complex manifolds Estimates of the Kobayashi metric on almost complex manifolds

2003-07-25

arxiv.org/abs/math/0307334v2

Mathematics

Complex Variables

date de redaction: 2003-4-3

Scientific paper

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 $M$.

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