Deformations of open stein manifolds

Abstract

We consider the deformation of the complex structure on an open Stein manifold. We show that a tame, compactly supported deformation of a Stein manifold is trivial. The remainder of our results are for deformations of the standard complex structure on Cn. A deformation of Cn which tends to a constant deformation faster that r-3 is trivial. Harmonic deformation tensors (w.r.t to the standard Euclidean metric) which are regular at infinity are constant.