How to reformulate this in a CVX way: Cube over Square

[Mark_L_Stone]

How can I write this kind of constraint (cube over square) in cvx

As shown above by @Michal_Adamaszek xy^2\geq z^3 with x,y,z\geq 0 is equivalent to sy\geq z^2,\ xz\geq s^2. The latter can be written in CVX as variables x y z s {z,s,y} == rotated_lorentz(1) {s,x,z} == rotated_lorentz(1) Then use x in place of z^3/y^2

My z is your y, and my y is your x.