Local removable singularity theorems for minimal laminations

Abstract

In this paper we prove a local removable singularity theorem for certain minimal laminations with isolated singularities in a Riemannian three-manifold. This removable singularity theorem is the key result used in our proof that a complete, embedded minimal surface in ${\mathbb{R}}^3$ with quadratic decay of curvature has finite total curvature.

41 pages, 8 figures