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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)

Citations:

Zbl 1076.53069
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