The space of embedded minimal surfaces of fixed genus in a 3manifold
II; Multivalued graphs in disks
Tobias H. Colding, William P. Minicozzi II,
2002.10.07
http://arxiv.org/abs/math/0210086
This paper is the second 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 3manifold. 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 $\RR^3$. We show here that
if the curvature of such a disk becomes large at some point, then it contains
an almost flat multivalued graph nearby that continues almost all the way to
the boundary.
