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Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds

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Abstract

For a compact Riemannian manifold M immersed into a higher dimensional manifold which can be chosen to be a Euclidean space, a unit sphere, or even a projective space, we successfully give several upper bounds in terms of the norm of the mean curvature vector of M for the first non-zero eigenvalue of the p-Laplacian (1 < p < +∞) on M. This result can be seen as an extension of Reilly’s bound for the first non-zero closed eigenvalue of the Laplace operator.

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Authors and Affiliations

  1. School of Mathematics and Physics Science, Jingchu University of Technology, Jingmen, 448000, China

    Feng Du

  2. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai, 264209, China

    Jing Mao

Authors
  1. Feng Du
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  2. Jing Mao
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Correspondence to Jing Mao.

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Du, F., Mao, J. Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds. Front. Math. China 10, 583–594 (2015). https://doi.org/10.1007/s11464-015-0422-x

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  • DOI: https://doi.org/10.1007/s11464-015-0422-x

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