Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 48, Number 1 (2004), 219-240.
On the first eigenvalue of the linearized operator of the higher order mean curvature for closed hypersurfaces in space forms
Luis J. Alías and J. Miguel Malacarne
Abstract
n this paper we derive sharp upper bounds for the first positive eigenvalue of the linearized operator of the higher order mean curvature of a closed hypersurface immersed into a Riemannian space form. Our bounds are extrinsic in the sense that they are given in terms of the higher order mean curvatures and the center(s) of gravity of the hypersurface, and they extend previous bounds recently given by Veeravalli [Ve] for the first positive eigenvalue of the Laplacian operator.
Article information
Source
Illinois J. Math., Volume 48, Number 1 (2004), 219-240.
Dates
First available in Project Euclid: 13 November 2009
Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258136182
Digital Object Identifier
doi:10.1215/ijm/1258136182
Mathematical Reviews number (MathSciNet)
MR2048223
Zentralblatt MATH identifier
1038.53061
Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 35P15: Estimation of eigenvalues, upper and lower bounds
Citation
Alías, Luis J.; Malacarne, J. Miguel. On the first eigenvalue of the linearized operator of the higher order mean curvature for closed hypersurfaces in space forms. Illinois J. Math. 48 (2004), no. 1, 219--240. doi:10.1215/ijm/1258136182. https://projecteuclid.org/euclid.ijm/1258136182
