The Structure of Complete Stable Minimal Surfaces in 3-Manifolds of Non-Negative Scalar Curvature ”

@inproceedings{FISCHERCOLBRIE2006TheSO,
title={The Structure of Complete Stable Minimal Surfaces in 3-Manifolds of Non-Negative Scalar Curvature ”},
author={DORIS FISCHER-COLBRIE and Richard M. Schoen},
year={2006}
}

The purpose of this paper is to study minimal surfaces in three-dimensional manifolds which, on each compact set, minimize area up to second order. If M is a minimal surface in a Riemannian three-manifold N, then the condition that M be stable is expressed analytically by the requirement that o n any compact domain of M, the first eigenvalue of the operator A+Ric(v)+(AI* be positive. Here Ric (v) is the Ricci curvature of N in the normal direction to M and (A)’ is the square of the length of… CONTINUE READING