biholomorphisms of strongly pseudoconvex domains extend to the boundary

It is a basic question in complex analysis to ask when does a biholomorphic mapping of two domains extend to the boundary. The following is a celebrated theorem of Fefferman for strongly pseudoconvex domains.

Theorem (Fefferman).

Let $U\mathrm{,}V\mathrm{\subset }{\mathrm{C}}^n$ ($n\mathrm{\ge }\mathrm{2}$) be two strongly pseudoconvex domains with smooth ($C^{\mathrm{\infty }}$) boundaries (the boundaries are smooth submanifolds). Let $f\mathrm{:}U\mathrm{\to }V$ be a biholomorphism. Then $f$ extends to a smooth diffeomorphism of $\overline{U}$ to $\overline{V}$.

Title	biholomorphisms of strongly pseudoconvex domains extend to the boundary
Canonical name	BiholomorphismsOfStronglyPseudoconvexDomainsExtendToTheBoundary
Date of creation	2013-03-22 16:44:30
Last modified on	2013-03-22 16:44:30
Owner	jirka (4157)
Last modified by	jirka (4157)
Numerical id	4
Author	jirka (4157)
Entry type	Theorem
Classification	msc 32T15
Related topic	LeviPseudoconvex