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)].


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)


Zbl 1076.53069
Full Text: DOI arXiv Euclid