Il a été observé par R. Kusner et prouvé par J. Ratzkin qu’on peut recoller ensemble deux surfaces à courbure moyenne constante ayant deux bouts de même paramètre de Delaunay. Cette procédure de recollement est connu comme « somme connexe bout-à-bout ». Dans ce papier, nous donnons une généralisation de cette construction en dimension quelconque dans le but de construire des nouvelles hypersurfaces à courbure moyenne constante à partir des hypersurfaces connues.
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.
@article{AFST_2009_6_18_4_717_0,
author = {Jleli, Mohamed},
title = {End-to-end gluing of constant mean curvature hypersurfaces},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {717--737},
publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 18},
number = {4},
year = {2009},
doi = {10.5802/afst.1222},
zbl = {1206.53010},
mrnumber = {2590386},
language = {en},
url = {http://www.numdam.org/articles/10.5802/afst.1222/}
}
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 PY - 2009 SP - 717 EP - 737 VL - 18 IS - 4 PB - Université Paul Sabatier, Institut de mathématiques PP - Toulouse UR - http://www.numdam.org/articles/10.5802/afst.1222/ DO - 10.5802/afst.1222 LA - en ID - AFST_2009_6_18_4_717_0 ER -
%0 Journal Article %A Jleli, Mohamed %T End-to-end gluing of constant mean curvature hypersurfaces %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2009 %P 717-737 %V 18 %N 4 %I Université Paul Sabatier, Institut de mathématiques %C Toulouse %U http://www.numdam.org/articles/10.5802/afst.1222/ %R 10.5802/afst.1222 %G en %F AFST_2009_6_18_4_717_0
Jleli, Mohamed. End-to-end gluing of constant mean curvature hypersurfaces. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 18 (2009) no. 4, pp. 717-737. doi : 10.5802/afst.1222. http://www.numdam.org/articles/10.5802/afst.1222/
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