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Inequalities for Eigenvalues of the Sub-Laplacian on Strictly Pseudoconvex CR Manifolds

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Abstract

The sub-Laplacian plays a key role in CR geometry. In this paper, we investigate eigenvalues of the sub-Laplacian on bounded domains of strictly pseudoconvex CR manifolds, strictly pseudoconvex CR manifolds submersed in Riemannian manifolds. We establish some Levitin–Parnovski-type inequalities and Cheng–Huang–Wei-type inequalities for their eigenvalues. As their applications, we derive some results for the standard CR sphere \(\mathbb{S}^{2n+1}\) in \(\mathbb{C}^{n+1}\), the Heisenberg group \(\mathbb{H}^n\), a strictly pseudoconvex CR manifold submersed in a minimal submanifold in \(\mathbb{R}^m\), domains of the standard sphere \(\mathbb{S}^{2n}\) and the projective space \(\mathbb{F}P^m\).

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Acknowledgments

The author would like to thank the reviewer for his or her valuable comments and suggestions.

Funding

This work was supported by the Fundamental Research Funds for the Central Universities (grant no. 30917011335) and the National Natural Science Foundation of China (grant no. 11001130).

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Authors and Affiliations

  1. Nanjing University of Science and Technology, Nanjing, 210094, China

    He-Jun Sun

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  1. He-Jun Sun
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Correspondence to He-Jun Sun.

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Sun, HJ. Inequalities for Eigenvalues of the Sub-Laplacian on Strictly Pseudoconvex CR Manifolds. Math Notes 109, 735–747 (2021). https://doi.org/10.1134/S0001434621050072

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  • DOI: https://doi.org/10.1134/S0001434621050072

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