A Remark on the Level Sets of the Graph of Harmonic Functions Bounded by Two Circles in Parallel Planes

In this paper,we find two auxiliary functions andmake use of themaximum principle to study the level sets of harmonic function defined on a convex ring with homogeneous Dirichlet boundary conditions in $mathbb{R}^2$. In higher dimensions, we also have a similar result to Jagy's.