In this paper, we review a number of uses of conformal mapping techniques for obtaining director profiles of liquid crystals in confined and semi-confined geometries. In particular, we will consider geometries which allow more than one stable state, some of which are of use in bistable displays. These solutions also allow the investigation of the energy of stable states and enable conclusions to be reached as to how such geometries may be optimised for bistable display applications. Such techniques are also able to provide initial configurations for the solution of more complicated situations where numerical methods are used to investigate switching characteristics.
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