no. 1
Construction of compact constant mean curvature hypersurfaces with topology
[Construction des hypersurfaces compactes à courbure moyenne constante qui ont une topologie non triviale]
Jleli, Mohamed1
1 Department of Mathematics College of Science King Saud University PO. Box 2455 Riyadh 11451 (Saudi Arabia)
Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 245-276.

Dans cet article, nous expliquons comment la méthode de construction dite “recollement des surfaces bout-à-bout” avec des resultats sur l’ensemble des hypersurfaces complètes non compactes à courbure moyenne constante qui ont un nombre fini de bouts de type Delaunay peuvent être utilisées pour construire des nouvelles familles d’hypersurfaces compactes à courbure moyenne constante qui ont une topologie non triviale.

In this paper, we explain how the end-to-end construction together with the moduli space theory can be used to produce compact constant mean curvature hypersurfaces with nontrivial topology. For the sake of simplicity, the hypersurfaces we construct have a large group of symmetry but the method can certainly be used to provide many more examples with less symmetries.

DOI : 10.5802/aif.2705
Classification : 35J05, 53A07, 53C21
Keywords: Mean curvature, Compact hypersurface
Mot clés : Courbure moyenne, hypersurface compacte
Jleli, Mohamed 1

1 Department of Mathematics College of Science King Saud University PO. Box 2455 Riyadh 11451 (Saudi Arabia) 
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Jleli, Mohamed. Construction of compact constant mean curvature hypersurfaces with topology. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 245-276. doi : 10.5802/aif.2705. http://www.numdam.org/articles/10.5802/aif.2705/

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