  We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the
limiting process we observe a continuous transition where the normal and
tangential parts of the Q-tensor decouple and various intrinsic and extrinsic
contributions emerge. Main properties of the thin film model, like uniaxiality
and parameter phase space, are preserved in the limiting process. For the
derived surface Landau-de Gennes model, we consider an L2-gradient flow. The
resulting tensor-valued surface partial differential equation is numerically
solved to demonstrate realizations of the tight coupling of elastic and bulk
free energy with geometric properties.
