By using Hessian matrix for x^4/y(y>=0), I confirm this matrix is semi-definite positve. But I don’t know which cvx expression can be used for x^4/y?

For example t\geq z^2/y,\ z\geq x^2, that is quad_over_lin and square.

Michal solution is the best.

However, alternatively

x \leq \mbox{geo_mean}(1,1,y,z)

should do the trick too.