Inequalities for eigenvalues of the biharmonic operator with weight on Riemannian manifolds

WANG, Qiaoling; XIA, Changyu

J. Math. Soc. Japan, Tome 62 (2010) no. 1, p. 597-622 / Harvested from Project Euclid

Résumé

Given a compact Riemannian manifold M with boundary (possibly empty), we consider the eigenvalues of the biharmonic operator with weight on M, proving a general inequality involving them. Using this inequality, we consider these eigenvalues when M is a compact domain of one of the following three spaces: 1) a complex projective space, 2) a minimal submanifold of a Euclidean space and 3) a minimal submanifold of a unit sphere.

Publié le : 2010-04-15
Classification: universal bounds, eigenvalues, biharmonic operator with weight, complex projective space, minimal submanifolds, sphere, Euclidean space, 53C20, 58G25, 35P15, 53C42

@article{1273236714,
     author = {WANG, Qiaoling and XIA, Changyu},
     title = {Inequalities for eigenvalues of the biharmonic operator with weight on Riemannian manifolds},
     journal = {J. Math. Soc. Japan},
     volume = {62},
     number = {1},
     year = {2010},
     pages = { 597-622},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1273236714}
}

WANG, Qiaoling; XIA, Changyu. Inequalities for eigenvalues of the biharmonic operator with weight on Riemannian manifolds. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp.  597-622. http://gdmltest.u-ga.fr/item/1273236714/