2 the Space of Embedded Minimal Surfaces of Fixed Genus in a 3-manifold I ; Estimates off the Axis for Disks

@inproceedings{Colding20022TS,
title={2 the Space of Embedded Minimal Surfaces of Fixed Genus in a 3-manifold I ; Estimates off the Axis for Disks},
author={Tobias Holck Colding and William P. Minicozzi},
year={2002}
}

This paper is the first in a series where we attempt to give a complete description of the space of all embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed Riemannian 3-manifold. The key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in R (with the flat metric). This study is undertaken here and completed in [CM6]; see also [CM8], [CM9] where we have surveyed our results… CONTINUE READING

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