  Given two Jordan curves in a Riemannian manifold, a minimal surface of
annulus type bounded by these curves is described as the harmonic extension of
a critical point of some functional (the Dirichlet integral) in a certain space
of boundary parametrizations. The $H^{2,2}$-regularity of the minimal surface
of annulus type will be proved by applying the critical points theory and
Morrey's growth condition.
