Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the associated family of Delaunay surfaces


Author: M. Kilian
Journal: Proc. Amer. Math. Soc. 132 (2004), 3075-3082
MSC (2000): Primary 53A10
DOI: https://doi.org/10.1090/S0002-9939-04-07483-0
Published electronically: May 12, 2004
MathSciNet review: 2063129
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 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

Similar Articles

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

Retrieve articles in all journals with MSC (2000): 53A10


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-04-07483-0
Keywords: Delaunay surfaces, DPW method
Received by editor(s): March 4, 2003
Published electronically: May 12, 2004
Communicated by: Jon G. Wolfson
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society