End-to-end gluing of constant mean curvature hypersurfaces

Mohamed Jleli[1]

  • [1] Département de mathématiques. Ecole supérieure des Sciences et Techniques de Tunis, 5 Avenue Taha Hussein 1008, Tunisia.

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

  • Volume: 18, Issue: 4, page 717-737
  • ISSN: 0240-2963

Abstract

top
It was observed by R. Kusner and proved by J. Ratzkin that one can connect together two constant mean curvature surfaces having two ends with the same Delaunay parameter. This gluing procedure is known as a “end-to-end connected sum”. In this paper we generalize, in any dimension, this gluing procedure to construct new constant mean curvature hypersurfaces starting from some known hypersurfaces.

How to cite

top

Jleli, Mohamed. "End-to-end gluing of constant mean curvature hypersurfaces." Annales de la faculté des sciences de Toulouse Mathématiques 18.4 (2009): 717-737. <http://eudml.org/doc/10125>.

@article{Jleli2009,
abstract = {It was observed by R. Kusner and proved by J. Ratzkin that one can connect together two constant mean curvature surfaces having two ends with the same Delaunay parameter. This gluing procedure is known as a “end-to-end connected sum”. In this paper we generalize, in any dimension, this gluing procedure to construct new constant mean curvature hypersurfaces starting from some known hypersurfaces.},
affiliation = {Département de mathématiques. Ecole supérieure des Sciences et Techniques de Tunis, 5 Avenue Taha Hussein 1008, Tunisia.},
author = {Jleli, Mohamed},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {constant mean curvature; hypersurfaces; end; necksize},
language = {eng},
month = {10},
number = {4},
pages = {717-737},
publisher = {Université Paul Sabatier, Toulouse},
title = {End-to-end gluing of constant mean curvature hypersurfaces},
url = {http://eudml.org/doc/10125},
volume = {18},
year = {2009},
}

TY - JOUR
AU - Jleli, Mohamed
TI - End-to-end gluing of constant mean curvature hypersurfaces
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2009/10//
PB - Université Paul Sabatier, Toulouse
VL - 18
IS - 4
SP - 717
EP - 737
AB - It was observed by R. Kusner and proved by J. Ratzkin that one can connect together two constant mean curvature surfaces having two ends with the same Delaunay parameter. This gluing procedure is known as a “end-to-end connected sum”. In this paper we generalize, in any dimension, this gluing procedure to construct new constant mean curvature hypersurfaces starting from some known hypersurfaces.
LA - eng
KW - constant mean curvature; hypersurfaces; end; necksize
UR - http://eudml.org/doc/10125
ER -

References

top
  1. Delaunay (C.).— Sur la surface de révolution dont la courbure moyenne est constante, Jour. de Mathématique, 6, p. 309-320 (1841). 
  2. Eells (J.).— The surfaces of Delaunay , Math. Intelligencer 9, no.1, p. 53-57 (1987). Zbl0605.53002MR869541
  3. Fakhi (S.) and Pacard (F.).— Existence result for minimal hypersurfaces with prescribed finite number of planar end , Manuscripta Mathematica, vol 103, issu 4, p. 465-512 (2000). Zbl0992.53011MR1811769
  4. Hsiang (W. Y.) and Yu (W. C.).— A generalization of a theorem of Delaunay, J. Differ. Geom. 16, No. 2, p. 161-177 (1981). Zbl0504.53044MR638783
  5. Jleli (M.).— Moduli space theory of constant mean curvature hypersurfaces. Journal of Advanced Nonlinear Studies, 9 p. 29-68 (2009). Zbl1180.53007MR2473148
  6. Jleli (M.) and Pacard (F.).— Construction of constant mean curvature hypersurfaces with prescribed finite number of Delaunay end. To appear. 
  7. Jleli (M.) and Pacard (F.).— An end-to-end construction for compact constant mean curvature surfaces Pacific Journal of Mathematics Vol. 221, No. 1, p. 81-108 (2005). Zbl1110.53043MR2194146
  8. Kapouleas (N.).— Complete constant mean curvature surfaces in Euclidean three-space, Ann. of Math. (2) 131, p. 239-330 (1990). Zbl0699.53007MR1043269
  9. Kapouleas (N.).— Compact constant mean curvature surfaces in Euclidean three-space, J. Differ. Geom. 33, No. 3, p. 683-715 (1991). Zbl0727.53063MR1100207
  10. Kapouleas (N.).— Constant mean curvature surfaces constructed by fusing Went tori, Invent. Math. 119, p. 443-518 (1995). Zbl0840.53005MR1317648
  11. Katsuei (K.).— Surfaces of revolution with prescribed mean curvature. Tohoku. Math. J ser 32, p. 147-153 (1980). Zbl0431.53005MR567837
  12. Katsuei (K.).— Surfaces of revolution with prescribed mean curvature. Tohoku. Math. J ser 32, p. 147-153 (1980). Zbl0431.53005MR567837
  13. Kusner (R.).— Bubbles conservations laws and balanced diagram , Geometric analysis and Computer graphics, (1991) 120-137. Springer-Verlag. MR1081331
  14. Kusner (R.), Mazzeo (R.) and Pollack (D.).— The moduli spaces of complete embeeded constant mean curvature surfaces , Geom. Funct. Anal. 6, p. 120-137 (1996). Zbl0966.58005MR1371233
  15. Mazzeo (R.) and Pacard (F.).— Constant mean curvature surfaces with Delaunay ends, Comm. Anal. Geom. 9No. 1 p. 169-237 (2001). Zbl1005.53006MR1807955
  16. Mazzeo (R.), Pacard (F.) and Pollack (D.).— Connected sums of constant mean curvature surfaces in Euclidiean 3 space, J.Reine Ang.Math. 536, p. 115.165 (2001). Zbl0972.53010MR1837428
  17. Mazzeo (R.), Pacard (F.) and Pollack (D.).— The conformal theory of Alexandrov embedded constant mean curvature surfaces in ℝ 3 , in Global theory of minimal surfaces, edited by D. Hoffman, Clay Mathematics Proceedings 2, Amer. Math. Soc, Providence, p. 525-559 (2005). Zbl1101.53006MR2167275
  18. Mazzeo (R.), Pollack (D.) and Uhlenbeck (K.).— Moduli spaces of singular Yammabe metrics , J. Amer. Math. 9, p. 303-344 (1996). Zbl0849.58012MR1356375
  19. Ratzkin (J.).— An end-to-end gluing construction for surfaces of constant mean curvature, PHD Thesis, University of Washington (2001). 
  20. Rosenberg (H.).— Hypersurfaces of constant mean curvature in space forms, Bull. Sc. math, série 2, 117, p. 211-239 (1993). Zbl0787.53046

NotesEmbed ?

top

You must be logged in to post comments.