Foliations by stationary discs of almost complex domains

Abstract. We study the problem of existence of stationary disks for domains in almost complex manifolds. As a consequence of our results, we prove that any almost complex domain which is a small deformation of a strictly linearly convex domain D ⊂ C^n with standard complex structure admits a singular foliation by stationary disks passing through any given internal point. Similar results are given for foliations by stationary disks through a given boundary point.