  Nematic interfaces are thin fluid films, ideally two-dimensional, endowed
with an in-plane degenerate nematic order. In this letter we examine a
generalisation of the classical Plateau problem to an axisymmetric nematic
interface bounded by two coaxial parallel rings. The equilibrium interface
shape results from the competition between surface tension, which favours the
minimization of the interface area, and the nematic elasticity which instead
promotes the alignment of the molecules along a common direction. We find two
classes of equilibrium solutions with intrinsically uniform alignments: one in
which the molecules are aligned along the meridians, the other along parallels.
Depending on two parameters, one geometric and the other constitutive, the
Gaussian curvature of the equilibrium interface may be negative, vanishing or
positive. The stability of these equilibrium configurations is investigated.
