Research article

Estimation of eigenvalues for the $ \alpha $-Laplace operator on pseudo-slant submanifolds of generalized Sasakian space forms

  • Received: 14 November 2021 Revised: 13 May 2022 Accepted: 01 June 2022 Published: 30 June 2022
  • MSC : 58C40, 53C42, 35P15

  • In this study, we seek to establish new upper bounds for the mean curvature and constant sectional curvature of the first positive eigenvalue of the $ \alpha $-Laplacian operator on Riemannian manifolds. More precisely, various methods are used to determine the first eigenvalue for the $ \alpha $-Laplacian operator on the closed oriented pseudo-slant submanifolds in a generalized Sasakian space form. From our findings for the Laplacian, we extend many Reilly-like inequalities to the $ \alpha $-Laplacian on pseudo slant submanifold in a unit sphere.

    Citation: Meraj Ali Khan, Ali H. Alkhaldi, Mohd. Aquib. Estimation of eigenvalues for the $ \alpha $-Laplace operator on pseudo-slant submanifolds of generalized Sasakian space forms[J]. AIMS Mathematics, 2022, 7(9): 16054-16066. doi: 10.3934/math.2022879

    Related Papers:

  • In this study, we seek to establish new upper bounds for the mean curvature and constant sectional curvature of the first positive eigenvalue of the $ \alpha $-Laplacian operator on Riemannian manifolds. More precisely, various methods are used to determine the first eigenvalue for the $ \alpha $-Laplacian operator on the closed oriented pseudo-slant submanifolds in a generalized Sasakian space form. From our findings for the Laplacian, we extend many Reilly-like inequalities to the $ \alpha $-Laplacian on pseudo slant submanifold in a unit sphere.



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