  We propose a continuum model to describe the molecular alignment in thin
nematic shells. By contrast with previous accounts, the two-dimensional free
energy, aimed at describing the physics of thin films of nematics deposited on
curved substrates, is not postulated but it is deduced from the conventional
three-dimensional theories of nematic liquid crystals. Both the director and
the order-tensor theories are taken into account. The so-obtained surface
energies exhibit extra terms compared to earlier models. These terms reflect
the coupling of the geometry of the shell with the nematic order parameters. As
expected, the shape of the shell plays a key role in the equilibrium
configurations of nematics coating it.
