The PDE describing constant mean curvature surfaces

Hongyou Wu

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 2, page 531-540
  • ISSN: 0862-7959

Abstract

top
We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.

How to cite

top

Wu, Hongyou. "The PDE describing constant mean curvature surfaces." Mathematica Bohemica 126.2 (2001): 531-540. <http://eudml.org/doc/248827>.

@article{Wu2001,
abstract = {We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.},
author = {Wu, Hongyou},
journal = {Mathematica Bohemica},
keywords = {constant mean curvature surfaces; nonlinear partial differential equation; dressing action; Weierstrass type representation; constant mean curvature surfaces; nonlinear partial differential equation; dressing action; Weierstrass type representation},
language = {eng},
number = {2},
pages = {531-540},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The PDE describing constant mean curvature surfaces},
url = {http://eudml.org/doc/248827},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Wu, Hongyou
TI - The PDE describing constant mean curvature surfaces
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 531
EP - 540
AB - We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.
LA - eng
KW - constant mean curvature surfaces; nonlinear partial differential equation; dressing action; Weierstrass type representation; constant mean curvature surfaces; nonlinear partial differential equation; dressing action; Weierstrass type representation
UR - http://eudml.org/doc/248827
ER -

References

top
  1. Constant mean curvature tori in terms of elliptic functions, J. Reine Angew. Math. 374 (1987), 169–192. (1987) Zbl0597.53003MR0876223
  2. 10.1007/BF01459243, Math. Ann. 290 (1991), 209–245. (1991) MR1109632DOI10.1007/BF01459243
  3. 10.1007/PL00004295, Math. Z. 224 (1997), 603–640. (1997) MR1452051DOI10.1007/PL00004295
  4. 10.2140/pjm.1998.182.229, Pacific J. Math. 182 (1998), 229–287. (1998) MR1609603DOI10.2140/pjm.1998.182.229
  5. 10.1007/BF02678186, Manuscripta Math. 92 (1997), 143–152. (1997) MR1428645DOI10.1007/BF02678186
  6. 10.4310/CAG.1998.v6.n4.a1, Comm. Anal. Geom. 6 (1998), 633–668. (1998) MR1664887DOI10.4310/CAG.1998.v6.n4.a1
  7. Constant mean curvature surfaces and loop groups, J. Reine Angew. Math. 440 (1993), 43–76. (1993) Zbl0779.53004MR1225957
  8. Differential Geometry of Curves and Surfaces, Prentice-Hall, Englewood Cliffs, NJ., 1976. (1976) Zbl0326.53001MR0394451
  9. 10.1007/BF03023575, Math. Intelligencer 9 (1987), 53–57. (1987) Zbl0605.53002MR0869541DOI10.1007/BF03023575
  10. 10.1007/BF02572424, Math. Z. 214 (1993), 527–565. (1993) MR1248112DOI10.1007/BF02572424
  11. Constant mean curvature surfaces with cylindrical ends, Mathematical Visualization. Algorithms, Applications, and Numerics. International workshop Visualization and mathematics, Berlin, Germany, September 16–19, 1997, Springer, Berlin, 1998, pp. 107–116. MR1677699
  12. 10.1080/10586458.1997.10504348, Experimental Math. 6 (1997), 13–32. (1997) MR1464579DOI10.1080/10586458.1997.10504348
  13. Differential Geometry in the Large, Springer, Berlin, 1983. (1983) Zbl0526.53002MR0707850
  14. 10.1007/BF02564507, Comment. Math. Helv. 69 (1994), 640–658. (1994) MR1303230DOI10.1007/BF02564507
  15. 10.2307/1971494, Ann. of Math. 131 (1990), 239–330. (1990) Zbl0699.53007MR1043269DOI10.2307/1971494
  16. 10.4310/jdg/1214446560, J. Differential Geom. 33 (1991), 683–715. (1991) Zbl0727.53063MR1100207DOI10.4310/jdg/1214446560
  17. 10.1007/BF01245190, Invent. Math. 119 (1995), 443–518. (1995) Zbl0840.53005MR1317648DOI10.1007/BF01245190
  18. 10.2307/1971425, Ann. of Math. 130 (1989), 407–451. (1989) MR1014929DOI10.2307/1971425
  19. A generalization of a theorem of Delaunay on constant mean curvature surfaces, Statistical Thermodynamics and Differential Geometry of Microstructured Materials, Springer, Berlin, 1993. (1993) Zbl0799.53010MR1226924
  20. 10.1512/iumj.1993.42.42057, Indiana Univ. Math. J. 42 (1993), 1239–1266. (1993) MR1266092DOI10.1512/iumj.1993.42.42057
  21. 10.2140/pjm.1986.121.193, Pacific J. Math. 121 (1986), 193–243. (1986) Zbl0586.53003MR0815044DOI10.2140/pjm.1986.121.193
  22. Immersed tori of constant mean curvature in ℝ 3 , Variational Methods for Free Surface Interfaces., P. Concus, R. Finn (eds.), Springer, New York, 1987, pp. 13–24. (1987) MR0872884
  23. Twisted tori of constant mean curvature in ℝ 3 , Seminar on New Results in Nonlinear Partial Differential Equations. Vieweg, Braunschweig, 1987, pp. 1–36. (1987) MR0896276
  24. 10.2748/tmj/1178225065, Tohoku Math. J. 49 (1997), 599–621. (1997) Zbl0912.53010MR1478919DOI10.2748/tmj/1178225065
  25. 10.1023/A:1006556302766, Ann. Global Anal. Geom. 17 (1999), 189–199. (1999) Zbl0954.58017MR1675409DOI10.1023/A:1006556302766
  26. 10.1007/BF03322110, Results Math. 36 (1999), 184–194. (1999) Zbl0946.58017MR1706520DOI10.1007/BF03322110

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.