New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms

Jiancheng Liu; Rong Mi

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 3, page 881-890
  • ISSN: 0011-4642

Abstract

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We study the first eigenvalue of the Jacobi operator on closed hypersurfaces with constant mean curvature in non-flat Riemannian space forms. Under an appropriate constraint on the totally umbilical tensor of the hypersurfaces and following Meléndez's ideas in J. Meléndez (2014) we obtain a new sharp upper bound of the first eigenvalue of the Jacobi operator.

How to cite

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Liu, Jiancheng, and Mi, Rong. "New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms." Czechoslovak Mathematical Journal 70.3 (2020): 881-890. <http://eudml.org/doc/296977>.

@article{Liu2020,
abstract = {We study the first eigenvalue of the Jacobi operator on closed hypersurfaces with constant mean curvature in non-flat Riemannian space forms. Under an appropriate constraint on the totally umbilical tensor of the hypersurfaces and following Meléndez's ideas in J. Meléndez (2014) we obtain a new sharp upper bound of the first eigenvalue of the Jacobi operator.},
author = {Liu, Jiancheng, Mi, Rong},
journal = {Czechoslovak Mathematical Journal},
keywords = {Jacobi operator; first eigenvalue; closed hypersurface},
language = {eng},
number = {3},
pages = {881-890},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms},
url = {http://eudml.org/doc/296977},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Liu, Jiancheng
AU - Mi, Rong
TI - New estimates for the first eigenvalue of the Jacobi operator on closed hypersurfaces in Riemannian space forms
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 3
SP - 881
EP - 890
AB - We study the first eigenvalue of the Jacobi operator on closed hypersurfaces with constant mean curvature in non-flat Riemannian space forms. Under an appropriate constraint on the totally umbilical tensor of the hypersurfaces and following Meléndez's ideas in J. Meléndez (2014) we obtain a new sharp upper bound of the first eigenvalue of the Jacobi operator.
LA - eng
KW - Jacobi operator; first eigenvalue; closed hypersurface
UR - http://eudml.org/doc/296977
ER -

References

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