A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifolds
Abstract
Description
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.
22 pages. to appear in Differ. Geom. Appl
22 pages. to appear in Differ. Geom. Appl