Curvature of Level Curves of Harmonic Functions

Abstract

Abstract If H is an arbitrary harmonic function defined on an open set Ω⊂ℂ, then the curvature of the level curves of H can be strictly maximal or strictly minimal at a point of Ω. However, if Ω is a doubly connected domain bounded by analytic convex Jordan curves, and if H is harmonic measure of Ω with respect to the outer boundary of Ω, then the minimal curvature of the level curves of H is attained on the boundary of Ω.