Find diffeomorphism from $\mathbb{R}^2$ onto
$U:= \{(u,v): \ u>v>0, \ uv<1\}$
$V:= \{u,v): \ u>v^2, \ u+v<6\}$ (or from $U,V$ onto $\mathbb{R}^2$).
Find diffeomorphism from $\mathbb{R}^2$ onto
$U:= \{(u,v): \ u>v>0, \ uv<1\}$
$V:= \{u,v): \ u>v^2, \ u+v<6\}$ (or from $U,V$ onto $\mathbb{R}^2$).