Estimates for eigenvalues of the bi-drifting Laplacian operator

• DOI: 10.1007/s00033-014-0426-5
• Publication Date: 2014-05-02T04:57:36Z
• Authors: Feng Du; Chuanxi Wu; Guanghan Li; Changyu Xia
• Keywords: Manifold (fluid mechanics); Operator (biology); Riemannian manifold

We prove universal inequalities of Payne–Polya–Weinberger–Yang type for eigenvalues of the bi-drifting Laplacian problem either on a compact Riemannian manifold with boundary (possibly empty) immersed in a Euclidean space, a unit sphere or a projective space or on bounded domains supporting some special functions of complete manifolds. In particular, such kind of inequalities for eigenvalues of the bi-drifting Laplacian on bounded domains in a Euclidean space are obtained. We also give universal inequalities of Payne–Polya–Weinberger–Yang type of this eigenvalue problem on bounded domains in a Gaussian shrinking soliton.