Let $f$ be a harmonic function in the complement of a Euclidean ball in $\mathbb{R}^n$. Let us assume that $f$ vanishes at infinity. 

**What assumptions on the decay rate at infinity imply that $f\equiv 0$?**

The case $n=3$ is of special interest to me.

Probably this is a very well studied question, but I am not a specialist.