## Illinois Journal of Mathematics

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

#### 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

https://projecteuclid.org/euclid.ijm/1258138155

Digital Object Identifier
doi:10.1215/ijm/1258138155

Mathematical Reviews number (MathSciNet)
MR1879239

Zentralblatt MATH identifier
0990.53058

#### 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