%0 Journal Article
%T Unstable minimal surfaces of annulus type in manifolds
%A Hwajeong Kim
%J Mathematics
%D 2006
%I arXiv
%X Unstable minimal surfaces are the unstable stationary points of the Dirichlet-Integral. In order to obtain unstable solutions, the method of the gradient flow together with the minimax-principle is generally used. The application of this method for minimal surfaces in the Euclidean spacce was presented in \cite{s3}. We extend this theory for obtaining unstable minimal surfaces in Riemannian manifolds. In particular, we handle minimal surfaces of annulus type, i.e. we prescribe two Jordan curves of class $C^3$ in a Riemannian manifold and prove the existence of unstable minimal surfaces of annulus type bounded by these curves.
%U http://arxiv.org/abs/math/0603615v2