The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus

Details The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus

2005-09-27

arxiv.org/abs/math/0509647v1

Mathematics

Differential Geometry

113 pages and 52 figures

Scientific paper

This paper is the fifth and final in a series on embedded minimal surfaces. Following our earlier papers on disks, we prove here two main structure theorems for non-simply connected embedded minimal surfaces of any given fixed genus. The first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely--oriented double spiral staircases. The second gives a pair of pants decomposition of any such surface when there are small necks, cutting the surface along a collection of short curves. After the cutting, we are left with graphical pieces that are defined over a disk with either one or two sub--disks removed (a topological disk with two sub--disks removed is called a pair of pants). Both of these structures occur as different extremes in the two-parameter family of minimal surfaces known as the Riemann examples. The results of [CM3]--[CM6] have already been used by many authors; see, e.g., the surveys [MeP], [P], [Ro] and the introduction in [CM6] for some of these applications. There is much current research on minimal surfaces with infinite topology. Some of the results of the present paper were announced previously and have already been widely used to study infinite topology minimal surfaces; see, e.g., [MeP], [MePRs1], [MePRs2], [MePRs3], and [P].

Affiliated with

Also associated with

No associations

Rating

The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The space of embedded minimal surfaces of fixed genus in a 3-manifold V; Fixed genus will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-238879