Local removable singularity theorems for minimal laminations

TL;DR

This paper proves a local removable singularity theorem for minimal laminations with isolated singularities, which is crucial for showing that certain complete minimal surfaces in three-dimensional space have finite total curvature.

Contribution

The paper introduces a new local removable singularity theorem for minimal laminations with isolated singularities in three-manifolds.

Findings

Proves a local removable singularity theorem for minimal laminations.

Establishes that complete embedded minimal surfaces with quadratic curvature decay have finite total curvature.

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.