Asymptotics in a Riemann-Hilbert boundary problem for pseudoholomorphic curves

where we x a volume element on to achieve the last isomorphism. The section (3) vanishes precisely at the complex points 2 . Such a point is called elliptic if @F ^ @F is transversal to the zero section in (4) and the intersection number int (@F^ @F; 0detF T 10M) is one, see [K], and general elliptic is de ned below in section 1. Our main result implies the following Corollary 2. Let F : 2 ,! (M; J) be an embedded real surface in an almost complex 4-manifold and 2 2 a general elliptic point. Then, for a neighborhood U of , there exists an embedded real hypersurface (N; 2 \ U; ) ,! (M; ; ) with a) N is Leviat and foliated by J-holomorphic curves of disc-type in (M;J) and boundary in .