Estimates of the Kobayashi metric on almost complex manifolds

arXivmath/0307334MaRDI QIDQ6473035

Hervé Gaussier, Alexandre Sukhov

Publication date: 25 July 2003

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 $M$.

Mathematics Subject Classification ID

Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Boundary regularity of mappings in several complex variables (32H40) Strongly pseudoconvex domains (32T15)

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