How to express the convex constraints?

1

x^(-k)<=(||q-u||^2+H^2)(||q-v||^2+H^2)
where k>0,x and q are optimization variables.

2

Not convex at all, even on the set where k=1,x=1,u=v=H=0.

4

This constraint is also not convex on the YALMIP forum, although YALMIP used with suitable solver can attempt to solve it.