A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifolds

AbstractGiven 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 H2,2-regularity of the minimal surface of annulus type will be proved by applying the critical points theory and Morrey's growth condition