The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks (Q1769552)

This important paper is the first in a series where the authors describe the space of all embedded minimal surfaces of fixed genus in a closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball in \(\mathbb{R}^3\). This study is undertaken here and completed in the fourth paper of this series [see Ann. Math. (2) 160, No. 2, 573-615 (2004; Zbl 1076.53069)].