Hwajeong Kim
Published 2006-03-27, updated 2008-05-30Version 2
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.
A variational approach to the regularity of minimal surfaces of annulus type in Riemannian manifolds
On conformal surfaces of annulus type
The $Q$-curvature on a 4-dimensional Riemannian manifold $(M,g)$ with $\int_MQdV_g=8π^2$
![QR code for arXiv:math/0603615 [math.DG]](http://oss.arxitics.com/images/favicon.svg)