Unstable minimal surfaces of annulus type in manifolds

2006/03/27 by Hwajeong Kim, Kim, Hwajeong
Mathematics · #49Q05 #58E05 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.AP #math.DG #msc:49Q05 #msc:58E05

paper · pdf · doi:10.48550/arxiv.math/0603615

36pages

openalex publication_date 2006/03/27 · arxiv created 2008/05/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \cites3. 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 C³ in a Riemannian manifold and prove the existence of unstable minimal surfaces of annulus type bounded by these curves.

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