2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68169We 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: 2003-4-3Complex VariablesDifferential Geometry32H02, 32H40, 32T15, 53C15text