Displaying similar documents to “Construction of compact constant mean curvature hypersurfaces with topology”

End-to-end gluing of constant mean curvature hypersurfaces

Mohamed Jleli (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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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.

Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in 𝕊 n + 1

Bingqing Ma, Guangyue Huang (2013)

Communications in Mathematics

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For compact hypersurfaces with constant mean curvature in the unit sphere, we give a comparison theorem between eigenvalues of the stability operator and that of the Hodge Laplacian on 1-forms. Furthermore, we also establish a comparison theorem between eigenvalues of the stability operator and that of the rough Laplacian.

Compact hypersurfaces with constant higher order mean curvatures.

Antonio Ros Mulero (1987)

Revista Matemática Iberoamericana

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A fundamental question about hypersurfaces in the Euclidean space is to decide if the sphere is the only compact hypersurface (embedded or immersed) with constant higher order mean curvature H, for some r = 1, ..., n.