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Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds

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Abstract

This paper studies eigenvalues of the drifting Laplacian on compact Riemannian manifolds with boundary (possibly empty) and provides a general inequality for them. Using the general inequality, we obtain universal inequalities for eigenvalues of the drifting Laplacian of Payne-Pólya-Weinberger-Yang type for manifolds supporting some special functions. We also obtain a lower bound for the first eigenvalue of the square of the drifting Laplacian on compact manifolds with boundary under some condition on the Bakry-Ricci curvature.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade de Brasília, 70910-900 , Brasília-DF, Brazil

    Changyu Xia

  2. Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Hongwei Xu

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  1. Changyu Xia
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  2. Hongwei Xu
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Correspondence to Changyu Xia.

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Xia, C., Xu, H. Inequalities for eigenvalues of the drifting Laplacian on Riemannian manifolds. Ann Glob Anal Geom 45, 155–166 (2014). https://doi.org/10.1007/s10455-013-9392-y

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  • DOI: https://doi.org/10.1007/s10455-013-9392-y

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