Constant mean curvature surfaces with Delaunay ends
Differential Geometry
2007-05-23 v1
Abstract
We construct a new class of complete constant mean curvature surfaces in R^3. These are geometrically different than the surfaces constructed by Kapouleas' gluing technique. These are obtained by piecing together half-Delaunay surfaces to the truncations of minimal k-noids. The gluing techniques are new: the surfaces are obtained by matching Cauchy data from the infinite dimensional family of exact solutions of the problem on each of the component pieces. These surfaces are also proved to be nondegenerate in the CMC moduli space.
Cite
@article{arxiv.math/9807039,
title = {Constant mean curvature surfaces with Delaunay ends},
author = {Rafe Mazzeo and Frank Pacard},
journal= {arXiv preprint arXiv:math/9807039},
year = {2007}
}