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http://dx.doi.org/10.4134/JKMS.j190737

LOWER ORDER EIGENVALUES FOR THE BI-DRIFTING LAPLACIAN ON THE GAUSSIAN SHRINKING SOLITON  

Zeng, Lingzhong (College of Mathematics and Informational Science Jiangxi Normal University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.6, 2020 , pp. 1471-1484 More about this Journal
Abstract
It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bi-drifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.
Keywords
Bi-drifting Laplacian; eigenvalues; Gaussian shrinking soliton;
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