Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Estimates for the higher eigenvalues of the drifting Laplacian on Hadamard manifolds
Xin XiongLingzhong ZengHuihui Zhu
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2022 Volume 45 Issue 1 Pages 143-156

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Abstract

In this paper, we investigate the eigenvalues of the drifting Laplacian on the bounded domain in Hardamard manifolds. By using upper half-plane model, we establish a universal inequality for the drifting Laplacian with a specific class of potential functions on the hyperbolic space, which can be viewed as a rigidity result associated with such a class of functions. Furthermore, we consider general Hardamard manifolds with pinching condition of sectional curvature, and obtain an eigenvalue inequality without the condition of Bakry-Émery curvature. As a by-product, we obtain a universal bound for the case of radial drifting Laplacian satisfying certain growth condition along with the radial direction.

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© 2022 Department of Mathematics, Tokyo Institute of Technology
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