• 제목/요약/키워드: Bi-drifting Laplacian

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

  • Zeng, Lingzhong
    • 대한수학회지
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    • 제57권6호
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    • pp.1471-1484
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    • 2020
  • 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.