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VOL. 10 | 2009 Constant Mean Curvature Surfaces in Euclidean and Minkowski Three-Spaces
David Brander, Wayne Rossman, Nicholas Schmitt

Editor(s) Ivaïlo M. Mladenov, Gaetano Vilasi, Akira Yoshioka

## Abstract

Spacelike constant mean curvature (CMC) surfaces in Minkowski three-space $\mathbb{L}^{3}$ have an infinite dimensional generalized Weierstrass representation. This is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group SU(2) with SU(1,1). The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop group, used to construct the surfaces, is not global. The construction is described here, with an emphasis on the difference from the Euclidean case.

## Information

Published: 1 January 2009
First available in Project Euclid: 13 July 2015

zbMATH: 1183.53005
MathSciNet: MR2757829

Digital Object Identifier: 10.7546/giq-10-2009-133-142