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arXiv:math/0603610 [math.DG]AbstractReferencesReviewsResources

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

Hwajeong Kim

Published 2006-03-27Version 1

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.

Comments: 22 pages. to appear in Differ. Geom. Appl
Categories: math.DG, math.AP
Subjects: 49Q05, 58E05
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