Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LOWER ORDER EIGENVALUES FOR THE BI-DRIFTING LAPLACIAN ON THE GAUSSIAN SHRINKING SOLITON

  • Zeng, Lingzhong (College of Mathematics and Informational Science Jiangxi Normal University)
  • Received : 2019.11.05
  • Accepted : 2020.05.18
  • Published : 2020.11.01
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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.

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References

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