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

A bi-harmonic function $u:U\to C$, where $U$ is an open subset of the complex plane $C$ is a solution of the equation $\Delta^2u=0$. Can a nonconstant bi-harmonic mapping have a constant modulus in an open set?

Example: The mapping $f(x)=x/|x|$ is a bi-harmonic mapping of the space $R^3$, so the answer to the above question for the space is YES.

share|cite|improve this question

It seems the answer is Yes as can be seen by the example $f(z)=z/\bar z$.

share|cite|improve this answer

Your Answer


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

Not the answer you're looking for? Browse other questions tagged or ask your own question.