Proceedings of the American Mathematical Society

Author(s): M. Kilian
Journal: Proc. Amer. Math. Soc. 132 (2004), 3075-3082.
MSC (2000): Primary 53A10
Posted: May 12, 2004
Retrieve article in: PDF

Abstract: We use the generalised Weierstraßrepresentation of Dorfmeister, Pedit and Wu to obtain the associated family of Delaunay surfaces and derive a formula for the neck size of the surface in terms of the entries of the holomorphic potential.

1.: C. Delaunay, Sur la surface de révolution dont la courbure moyenne est constante, J. Math. Pures et Appl. Sér. 1 6 (1841), 309-320.
2.: J. Dorfmeister and G. Haak, Construction of non-simply connected CMC surfaces via dressing, J. Math. Soc. Japan, 55 (2003), no. 2, 335-364. MR 2004d:53010
3.: -, On constant mean curvature surfaces with periodic metric, Pacific J. Math. 182 (1998), 229-287. MR 99f:53007
4.: J. Dorfmeister, F. Pedit, and H. Wu, Weierstrass type representation of harmonic maps into symmetric spaces, Comm. Anal. Geom. 6 (1998), no. 4, 633-668. MR 2000d:53099
5.: J. Eells, The surfaces of Delaunay, Math. Intelligencer 9 (1987), 53-57.MR 88h:53011
6.: M. Kilian, Constant mean curvature cylinders, Ph.D. thesis, Univ. of Massachusetts, Amherst, 2000.
7.: M. Kilian, I. McIntosh, and N. Schmitt, New constant mean curvature surfaces, Experiment. Math. 9 (2000), no. 4, 595-611. MR 2002e:53008
8.: M. Kilian, N. Schmitt, and I. Sterling, Dressing CMC n-Noids, Math. Z. 246 (2004), no. 3, 501-519.
9.: N. Korevar, R. Kusner, and B. Solomon, The structure of complete embedded surfaces with constant mean curvature, J. Diff. Geom. 30 (1989), no. 2, 465-503. MR 90g:53011
10.: I. McIntosh, Global solutions of the elliptic 2d periodic Toda lattice, Nonlinearity 7 (1994), no. 1, 85-108. MR 95g:58108
11.: E. A. Ruh and J. Vilms, The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569-573. MR 41:4400
12.: N. Schmitt, CMCLab, http://www.gang.umass.edu/software.
13.: -, Constant mean curvature trinoids, arXiv:math.DG/0403036.
14.: B. Smyth, A generalization of a theorem of Delaunay on constant mean curvature surfaces, IMA Vol. Math. Appl. 51 (1993), 123-130. MR 94f:53012
15.: K. Uhlenbeck, Harmonic maps into lie groups (classical solutions of the chiral model), J. Diff. Geom. 30 (1989), 1-50. MR 90g:58028

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53A10

M. Kilian
Affiliation: Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
Email: masmk@maths.bath.ac.uk

DOI: 10.1090/S0002-9939-04-07483-0
PII: S 0002-9939(04)07483-0
Keywords: Delaunay surfaces, DPW method
Received by editor(s): March 4, 2003
Posted: May 12, 2004
Communicated by: Jon G. Wolfson
Copyright of article: Copyright 2004, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS