Minimal strings of above language are : $\color{green}{aaab, aabb}$ and $\color{green}{abbb}$ as minimal value of $m$ and $n$ is $1$, and also $mn \ge 3$.
Minimal pairs of $m$ and $n$ that satisfy above constraints are: $(m,n) = (1,3), (3,1)$ and $(2,2)$
So, RegExp would be : $\color{maroon}{aa^*bbbb^* + aaaa^*bb^* + aaa^*bbb^*}$