Unstable minimal surfaces of annulus type in manifolds

Details Unstable minimal surfaces of annulus type in manifolds Unstable minimal surfaces of annulus type in manifolds

2006-03-27

arxiv.org/abs/math/0603615v2

Mathematics

Differential Geometry

36pages

Scientific paper

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.

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