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Global minimisers of cholesteric liquid crystal systems

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.