On the convexity of a solution of Liouville's equation (Q2640041)

The author gives a new proof for the convexity of the solution to \(\Delta h=4e^{2h}\) in \(\Omega\), where \(\Omega\) is a convex plane domain. The proof uses complex variable methods. The author also discusses the connection to other domain functions and the interpretation of h in terms of vortex motion.