Subharmonic functions outside a compact set in $\textbf {R}^{n}$

Abstract:

Let $u$ be a subharmonic function defined outside a compact set in ${{\mathbf {R}}^2}$. Then $u$ is of the form $u(x) = s(x) - \alpha \log \left | x \right |$ outside a disc where $s(x)$ is a nonconstant subharmonic function in ${{\mathbf {R}}^2}$ and $\alpha \geqslant 0$. Some applications and the analogues in ${{\mathbf {R}}^n}$, $n \geqslant 3$, are given.