MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am wondering if anything is known about this. I couldn't find anything in the literature.

In '74 C. Fefferman published a solution to the following problem. Let $\sigma:D\rightarrow D$ be an automorphism of a strictly pseudoconvex domanain $D\subset\mathbb{C}^n$. Then $\sigma$ extends to a smooth map $\sigma:\overline{D}\rightarrow\overline{D}$.

My question: Is anything known about this problem for a strictly pseudoconvex domain $D\subset M$ in a complex manifold $M$?

I have an idea of how to prove it for $K_M >0$, i.e. positive canonical bundle. Fefferman's approach used the Bergman metric. The Bergman metric is nondegenerate for more general domains only if $K_M$ is very ample, which is too strong an assumption to be very interesting.

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.