Displaying similar documents to “Sharp eigenvalue estimates of closed H -hypersurfaces in locally symmetric spaces”

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.

Hypersurfaces with constant curvature in ℝ n + 1

J. A. Gálvez, A. Martínez (2002)

Banach Center Publications

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We give some optimal estimates of the height, curvature and volume of compact hypersurfaces in ℝ n + 1 with constant curvature bounding a planar closed (n-1)-submanifold.

Hypersurfaces with constant k -th mean curvature in a Lorentzian space form

Shichang Shu (2010)

Archivum Mathematicum

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In this paper, we study n ( n ≥ 3 ) -dimensional complete connected and oriented space-like hypersurfaces M n in an (n+1)-dimensional Lorentzian space form M 1 n + 1 ( c ) with non-zero constant k -th ( k < n ) mean curvature and two distinct principal curvatures λ and μ . We give some characterizations of Riemannian product H m ( c 1 ) × M n - m ( c 2 ) and show that the Riemannian product H m ( c 1 ) × M n - m ( c 2 ) is the only complete connected and oriented space-like hypersurface in M 1 n + 1 ( c ) with constant k -th mean curvature and two distinct principal curvatures, if the multiplicities...