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

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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

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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

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  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
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