Inequalities for eigenvalues of the biharmonic operator with weight on Riemannian manifolds
Qiaoling WANG and Changyu XIA
Source: J. Math. Soc. Japan Volume 62, Number 2
(2010), 597-622.
Abstract
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.
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Keywords: universal bounds; eigenvalues; biharmonic operator with weight; complex projective space; minimal submanifolds; sphere; Euclidean space
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