Published in Complex Variables and Elliptic Equations, Volume 52, Issue 8 August 2007, 741-754.

Abstract : We construct some lift of an almost complex structure to the cotangent bundle, using a connection on the base manifold. This unifies the complete lift defined by I.Sato and the horizontal lift introduced by S.Ishihara and K.Yano. We study some geometric properties of this lift and its compatibility with symplectic forms on the cotangent bundle.

Published in Journal of Mathematical Analysis and Applications, Volume 345, Issue 2, September 2008, 825-844.

Abstract : Let D be a smooth relatively compact domain in a four dimensional almost complex manifold (M,J). We give sharp estimates of the Kobayashi metric. Our approach is based on a local quantitative description of both the domain D and the almost complex structure J near a boundary point. Following Z.M.Balogh and M.Bonk, these sharp estimates provide the Gromov hyperbolicity of the domain D.

To be published in Mathematische Zeitschrift.

Abstract : Let D be a J-pseudoconvex region in a smooth almost complex manifold (M,J) of real dimension four. We construct a local peak J plurisubharmonic function at every boundary point p of finite D'Angelo type. As applications we give local estimates of the Kobayashi pseudometric, implying the local Kobayashi hyperbolicity of D at p. In case the point p is of D'Angelo type less than or equal to four, or the approach is nontangential, we provide sharp estimates of the Kobayashi pseudometric.

Submitted.

Abstract : We study the asymptotic behaviour of pseudoholomorphic discs contained into smooth J-pseudoconvex regions of finite type into an almost complex manifold (M,J) of real dimension four.