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

Hwajeong Kim
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Abstract

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.

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Hwajeong Kim. 2006-03-27. A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifolds. https://arxiv.org/abs/math/0603610

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