Colding, Tobias H.; Minicozzi, William P. II The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks. (English) Zbl 1070.53031 Ann. Math. (2) 160, No. 1, 27-68 (2004). 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)]. Reviewer: Li Haizhong (Beijing) Cited in 4 ReviewsCited in 39 Documents 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 Citations:Zbl 1076.53069 PDFBibTeX XMLCite \textit{T. H. Colding} and \textit{W. P. Minicozzi II}, Ann. Math. (2) 160, No. 1, 27--68 (2004; Zbl 1070.53031) Full Text: DOI arXiv Euclid