The conformal theory of Alexandrov embedded constant mean curvature surfaces in $R^3$

Details The conformal theory of Alexandrov embedded constant mean curvature surfaces in $R^3$ The conformal theory of Alexandrov embedded constant mean curvature surfaces in $R^3$

2001-10-09

arxiv.org/abs/math/0110099v1

Mathematics

Differential Geometry

32 pages

Scientific paper

We first prove a general gluing theorem which creates new nondegenerate constant mean curvature surfaces by attaching half Delaunay surfaces with small necksize to arbitrary points of any nondegenerate CMC surface. The proof uses the method of Cauchy data matching from \cite{MP}, cf. also \cite{MPP}. In the second part of this paper, we develop the consequences of this result and (at least partially) characterize the image of the map which associates to each complete, Alexandrov-embedded CMC surface with finite topology its associated conformal structure, which is a compact Riemann surface with a finite number of punctures. In particular, we show that this `forgetful' map is surjective when the genus is zero. This proves in particular that the CMC moduli space has a complicated topological structure. These latter results are closely related to recent work of Kusner \cite{Ku}.

Affiliated with

Also associated with

No associations

Rating

The conformal theory of Alexandrov embedded constant mean curvature surfaces in $R^3$ 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 conformal theory of Alexandrov embedded constant mean curvature surfaces in $R^3$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The conformal theory of Alexandrov embedded constant mean curvature surfaces in $R^3$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-396526