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

Bingqing Ma; Guangyue Huang

Communications in Mathematics (2013)

  • Volume: 21, Issue: 1, page 31-38
  • ISSN: 1804-1388

Abstract

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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.

How to cite

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Ma, Bingqing, and Huang, Guangyue. "Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in $\mathbb {S}^{n+1}$." Communications in Mathematics 21.1 (2013): 31-38. <http://eudml.org/doc/260607>.

@article{Ma2013,
abstract = {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.},
author = {Ma, Bingqing, Huang, Guangyue},
journal = {Communications in Mathematics},
keywords = {hypersurface with constant mean curvature; the stability operator; Hodge Laplacian; rough Laplacian; hypersurface with constant mean curvature; the stability operator; Hodge Laplacian; rough Laplacian},
language = {eng},
number = {1},
pages = {31-38},
publisher = {University of Ostrava},
title = {Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in $\mathbb \{S\}^\{n+1\}$},
url = {http://eudml.org/doc/260607},
volume = {21},
year = {2013},
}

TY - JOUR
AU - Ma, Bingqing
AU - Huang, Guangyue
TI - Eigenvalue relationships between Laplacians of constant mean curvature hypersurfaces in $\mathbb {S}^{n+1}$
JO - Communications in Mathematics
PY - 2013
PB - University of Ostrava
VL - 21
IS - 1
SP - 31
EP - 38
AB - 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.
LA - eng
KW - hypersurface with constant mean curvature; the stability operator; Hodge Laplacian; rough Laplacian; hypersurface with constant mean curvature; the stability operator; Hodge Laplacian; rough Laplacian
UR - http://eudml.org/doc/260607
ER -

References

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