Stationary level surfaces and Liouville-type theorems characterizing hyperplanes

Shigeru Sakaguchi

We consider an entire graph $S$ in ${\mathbb{R}}^{N+1}$ of a continuous real function $f$ over ${\mathbb{R}}^N$ with $N\ge 1$. Let $\Omega$ be an unbounded domain in ${\mathbb{R}}^{N+1}$ with…