Universal bounds for eigenvalues of the polydrifting Laplacian operator in compact domains in the $$\mathbb {R}^{n}$$ R n and $$\mathbb {S}^{n}$$ S n

Abstract

In this paper, we study eigenvalues of polydrifting Laplacian on compact Riemannian manifolds with boundary (possibly empty). Here, we prove a universal inequality for the eigenvalues of the polydrifting operator on compact domains in an Euclidean space \(\mathbb {R}^{n}\). In particular our result covers the Jost–Xia inequality for polyharmonic operator. Moreover universal inequalities for eigenvalues of polydrifting operator on compact domains in a unit \(n\)-sphere \(\mathbb {S}^{n}\) are given.