Extrinsic estimates for eigenvalues of the Laplace operator

CHEN, Daguang; CHENG, Qing-Ming

J. Math. Soc. Japan, Tome 60 (2008) no. 1, p. 325-339 / Harvested from Project Euclid

Résumé

For a bounded domain in a complete Riemannian manifold $M^n$ isometrically immersed in a Euclidean space, we derive extrinsic estimates for eigenvalues of the Dirichlet eigenvalue problem of the Laplace operator, which depend on the mean curvature of the immersion. Further, we also obtain an upper bound for the $(k+1)^{\text{th}}$ eigenvalue, which is best possible in the meaning of order on $K$ .

Publié le : 2008-04-15
Classification: universal inequality for eigenvalues, Yang-type inequality, trial function, 35P15, 58C40

@article{1212156653,
     author = {CHEN, Daguang and CHENG, Qing-Ming},
     title = {Extrinsic estimates for eigenvalues of the Laplace operator},
     journal = {J. Math. Soc. Japan},
     volume = {60},
     number = {1},
     year = {2008},
     pages = { 325-339},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1212156653}
}

CHEN, Daguang; CHENG, Qing-Ming. Extrinsic estimates for eigenvalues of the Laplace operator. J. Math. Soc. Japan, Tome 60 (2008) no. 1, pp.  325-339. http://gdmltest.u-ga.fr/item/1212156653/