  Thin cylindrical tethers are common lipid bilayer membrane structures,
arising in situations ranging from micromanipulation experiments on artificial
vesicles to the dynamic structure of the Golgi apparatus. We study the shape
and formation of a tether in terms of the classical soap-film problem, which is
applied to the case of a membrane disk under tension subject to a point force.
A tether forms from the elastic boundary layer near the point of application of
the force, for sufficiently large displacement. Analytic results for various
aspects of the membrane shape are given.
