Recent advances in the global theory of constant mean curvature surfaces

Rafe Mazzeo

Recent advances in the global theory of constant mean curvature surfaces

Differential Geometry 2007-05-23 v1

Authors: Rafe Mazzeo

Abstract

The theory of complete surfaces of (nonzero) constant mean curvature in $\RR^3$ has progressed markedly in the last decade. This paper surveys a number of these developments in the setting of Alexandrov embedded surfaces; the focus is on gluing constructions and moduli space theory, and the analytic techniques on which these results depend. The last section contains some new results about smoothing the moduli space and about CMC surfaces in asymptotically Euclidean manifolds.

Keywords

constant mean curvature surfaces alexandrov embedded surfaces gluing constructions moduli space cmc surfaces asymptotically euclidean manifolds

Cite

@article{arxiv.math/0209330,
  title  = {Recent advances in the global theory of constant mean curvature surfaces},
  author = {Rafe Mazzeo},
  journal= {arXiv preprint arXiv:math/0209330},
  year   = {2007}
}

Comments

29 pages. Written for the Proceedings of the Conference in Honor of Haim Brezis and Felix Browder, Oct. 2001

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