  Free interfaces of liquid crystals tend to minimise both capillarity and
anchoring forces. Here we study nematic films in planar and radial geometries
with antagonistic anchoring boundary conditions and one deformable interface.
Assuming a perturbation ansatz we study possible couplings of the director
configuration with the shape of free interfaces. In the long-wavelength limit
independent of the surface tension, we find analytically threshold thickness
when flat film becomes unstable. Next we quantify the bifurcation of a circular
ring towards structures with $m$-fold rotational symmetry, induced by elastic
anisotropy of nematic director in the bulk. We believe that our simplified
approach can give additional insight into elastic and capillary phenomena of
materials with inherent liquid crystalline order and free interfaces.
