We study the eigenvalues of the biharmonic operators and the buckling eigenvalue on complete, open Riemannian manifolds. We show that the first eigenvalue of the biharmonic operator on a complete, parabolic Riemannian manifold is zero. We give a generalization of the buckling eigenvalue and give applications to studying the stability of minimal Lagrangian submanifolds in Kähler manifolds.
@article{1113247128,
author = {Palmer, Bennett},
title = {Biharmonic capacity and the stability of minimal Lagrangian submanifolds},
journal = {Tohoku Math. J. (2)},
volume = {55},
number = {2},
year = {2003},
pages = { 529-541},
language = {en},
url = {http://dml.mathdoc.fr/item/1113247128}
}
Palmer, Bennett. Biharmonic capacity and the stability of minimal Lagrangian submanifolds. Tohoku Math. J. (2), Tome 55 (2003) no. 2, pp. 529-541. http://gdmltest.u-ga.fr/item/1113247128/