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.
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R. G. Pereira was supported in part by CAPES/REUNI. L. Adriano was supported by CAPES/PNPD and FAPEG. R. Pina was supported by CAPES/PROCAD and FAPEG.
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Pereira, R.G., Adriano, L. & Pina, R. Universal bounds for eigenvalues of the polydrifting Laplacian operator in compact domains in the \(\mathbb {R}^{n}\) and \(\mathbb {S}^{n}\) . Ann Glob Anal Geom 47, 373–397 (2015). https://doi.org/10.1007/s10455-015-9450-8
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DOI: https://doi.org/10.1007/s10455-015-9450-8