The existence of a \(\mu\)-holomorphic separating function on bounded smooth domains (Q1206127)

The authors prove that for a bounded smoothly domain \(\Omega\) there is a new complex structure on it under which \(\Omega\) will locally become a strongly convex even though the point on \(b\Omega\) is not a pseudoconvex point from the view of the original complex structure. Particularly if \(\Omega\) is a weakly pseudoconvex domain, the \(\mu\) can be made sufficiently close to the original complex structure. Therefore a lot of properties of strongly pseudoconvex domains will become true on weakly pseudoconvex domains, or general domains. For example, it is proved here that there is a \(\mu\)-holomorphic separating function which is holomorphic under the new complex structure.