On conjugate pseudo-harmonic functions

Abstract

We prove the following theorem. Let $U$ be a pseudo-harmonic function on a surface $M^2$. For a real valued continuous function $V:M^2\to \mathbb{R}$ to be a conjugate pseudo-harmonic function of $U$ on $M^2$ it is necessary and sufficient that $V$ is open on level sets of $U$.

9 pages, 2 figures