## The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks.(English)Zbl 1070.53031

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)].

### MSC:

 53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) 58D10 Spaces of embeddings and immersions 58E12 Variational problems concerning minimal surfaces (problems in two independent variables)

### Keywords:

embedded minimal surfaces; genus; space

Zbl 1076.53069
Full Text: