Illinois Journal of Mathematics

Upper bounds for the first eigenvalue of the operator $L\sb r$ and some applications

Hilário Alencar, Fernando Marques, and Manfredo do Carmo

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Abstract

We obtain upper bounds for the first eigenvalue of the linearized operator $L_r$ of the $r$-mean curvature of a compact manifold immersed in a space of constant curvature $\delta$. By the same method, we obtain an upper bound for the first eigenvalue of the stability operator associated to $L_r$ when $\delta < 0$.

Article information

Source
Illinois J. Math., Volume 45, Number 3 (2001), 851-863.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138155

Digital Object Identifier
doi:10.1215/ijm/1258138155

Mathematical Reviews number (MathSciNet)
MR1879239

Zentralblatt MATH identifier
0990.53058

Subjects
Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]
Secondary: 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]

Citation

Alencar, Hilário; do Carmo, Manfredo; Marques, Fernando. Upper bounds for the first eigenvalue of the operator $L\sb r$ and some applications. Illinois J. Math. 45 (2001), no. 3, 851--863. doi:10.1215/ijm/1258138155. https://projecteuclid.org/euclid.ijm/1258138155


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