Proper J-holomorphic discs in Stein domains of dimension 2
We prove the existence of global Bishop discs in a strictly pseudoconvex Stein domain in an almost complex manifold of complex dimension 2.
math.CV↗
arXiv subjects
Bernard Coupet
Publications and source records attributed to Bernard Coupet.
Some aspects of analysis on almost complex manifolds with boundary
We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds and the elliptic regularity of some diffeomorphisms in almost complex manifolds with boundary.
math.CV↗
Fefferman's mapping theorem on almost complex manifolds
We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds. The proof is mainly based on a reflection principle for pseudoholomorphic discs, on precise estimates of the Kobayashi-Royden infinitesimal pseudometric and on the scaling method in almost complex manifolds.
math.CV↗