Geodesic
Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in $\mathbb{S}^{n+1}$
Communications in Mathematics, Tome 21 (2013) no. 1, pp. 31-38

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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.
Classification : 58J50
Keywords: hypersurface with constant mean curvature; the stability operator; Hodge Laplacian; rough Laplacian 
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     author = {Ma, Bingqing and Huang, Guangyue},
     title = {Eigenvalue relationships between {Laplacians} of constant mean curvature hypersurfaces in $\mathbb{S}^{n+1}$},
     journal = {Communications in Mathematics},
     pages = {31--38},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
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     zbl = {06202723},
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     url = {http://geodesic.mathdoc.fr/item/COMIM_2013__21_1_a2/}
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Ma, Bingqing; Huang, Guangyue. Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in $\mathbb{S}^{n+1}$. Communications in Mathematics, Tome 21 (2013) no. 1, pp. 31-38. http://geodesic.mathdoc.fr/item/COMIM_2013__21_1_a2/