The space of embedded minimal surfaces of fixed genus in a 3manifold
III; Planar domains
Tobias H. Colding, William P. Minicozzi II,
2002.10.09
http://arxiv.org/abs/math/0210141
This paper is the third in a series where we describe the space of all
embedded minimal surfaces of fixed genus in a fixed (but arbitrary) closed
3manifold. In [CM3][CM5] we describe the case where the surfaces are
topologically disks on any fixed small scale. To describe general planar
domains (in [CM6]) we need in addition to the results of [CM3][CM5] a key
estimate for embedded stable annuli which is the main result of this paper.
This estimate asserts that such an annulus is a graph away from its boundary if
it has only one interior boundary component and if this component lies in a
small (extrinsic) ball.
