Convexity of level lines of Martin functions and applications

A. -K. Gallagher, J. Lebl, K. Ramachandran

Let $\Omega$ be an unbounded domain in $\mathbb{R}\times {\mathbb{R}}^d.$ A positive harmonic function $u$ on $\Omega$ that vanishes on the boundary of $\Omega$ is called a Martin function. In thi…