How to express 1/(y *(1-x)) in CVX, and y>0; 0<x<1 are the constraints

How to express 1/(y *(1-x)) in CVX, and y>0; 0<x<1 are the constraints.
I calculated the Hessian matric

Assume you need
t \geq \frac{1}{x*z},\quad x,z\geq 0.
Therefore,
(t*x*z)^{1/3} \geq 1
implying the geometric mean of (t,x,z) must be greater than one.

As far as I remember there is geo_mean function in cvx.

Yes, geo_mean([t,y,1-x]) >= 1 can be used Then use t in place of 1/(y*(1-x)) .

Alternatively, prod_inv([y,1-x]) can be directly used in place of 1/(y*(1-x)) . CVX converts this under the hood to the geo_mean formulation.