MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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

Let $D \subseteq \mathbb{C}^n$ be a bounded domain and let $t \in D$. We say that $D$ is a minimal domain with center $t$ if for each biholomorphism $F:D \to D' \subseteq \mathbb{C}^n$ such that $JF(t) = 1$ ($JF$ denotes the complex jacobian), we have $vol(D) \leq vol(D')$. I need to prove that a necessary and sufficient criterion for a domain $D$ to be minimal with center $t$ is $K(z,t) = \frac{1}{vol(D)}$, where $K$ is the Bergman kernel function of $D$. The sufficiency follows from the second extremal property of the Bergman kernel function mentioned here. How do I prove the converse?

share|cite|improve this question

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.