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

## References

• 1 Fefferman, Charles. . Invent. Math. 26 (1974), 1–65.
• 2 Steven G. Krantz. , AMS Chelsea Publishing, Providence, Rhode Island, 1992.
Title biholomorphisms of strongly pseudoconvex domains extend to the boundary BiholomorphismsOfStronglyPseudoconvexDomainsExtendToTheBoundary 2013-03-22 16:44:30 2013-03-22 16:44:30 jirka (4157) jirka (4157) 4 jirka (4157) Theorem msc 32T15 LeviPseudoconvex