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

Let $f,g$ be a pair of univalent functions on a proper subdomain $\Omega$ of $\mathbb C$. Does their sum $f+g$ necessarily omit any complex value? Similarly, can all holomorphic function be written as sums of univalent functions?

share|cite|improve this question
No to both in as simple domain as the unit disk. 1) $(1-z)^{-2}-(1+z)^{-2}$ 2) Univalent functions cannot grow too fast near the boundary. – fedja Jun 16 '12 at 0:36
Or $z$ and $1/z$ on ${\bf C} - \{0\}$. – Nik Weaver Jun 16 '12 at 0:42

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.