# 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 $\overline{V}$.

## 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 |
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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 |