  In this paper we examine the modelling and minimisation of cholesteric liquid
crystals systems within the Oseen-Frank theory. We focus on a cuboid domain
with the frustrated boundary conditions ${\bf n}(0,x,y)=(1,0,0)$ and ${\bf
n}(1,x,y)=(0,0,1)$. With general elastic constants, we find the unique global
minimisers amongst functions of one variable and prove that these are global
minimisers of the entire problem if the cholesteric pitch is sufficiently long.
Finally we show that our analysis easily translates over the study the global
stability of the constant state ${\bf n}(x,y,z) = (0,0,1)$ with unfrustrated
boundary conditions.
