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Research Article | Open Access

The upper bound for the first positive eigenvalue of Sub-Laplacian on a compact strictly pseudoconvex hypersurface

Guijuan Lin1( ), Sujuan Long2, Qiqi Zhang3
School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China
School of Computer and Data Science, Minjiang University, Fuzhou 350108, China
School of Mathematics and Imformation Science, Nanchang Hangkong University, Nanchang 330063, China
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Abstract

Let (M2n+1,θ) be a compact strictly pseudoconvex real hypersurfaces equipped with the pseudohermitian structure θ, and λ1 be the first positive eigenvalue of sub-Laplacian Δb on (M2n+1,θ). In this paper, we will give the upper bound of λ1 under certain conditions that " ReΔb(ρj+ρj¯)(2Δ~ρρj+|∂ρ|ρ2n−1ρkρjk)≤0 (for some j)" or " ρjk¯=δjk" holds, and apply these results to the ellipsoids furthermore.

Keywords

sub-Laplacianupper boundthe first positive eigenvaluecompact real hypersurfacesellipsoids
CLC number: 32V05, 32V15, 32V20

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AIMS Mathematics
Volume 9 Issue 9,
September 2024
Pages 25376-25395
DOI: 10.3934/math.20241239

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Lin G, Long S, Zhang Q. The upper bound for the first positive eigenvalue of Sub-Laplacian on a compact strictly pseudoconvex hypersurface. AIMS Mathematics, 2024, 9(9): 25376-25395. https://doi.org/10.3934/math.20241239

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Received: 22 July 2024
Revised: 21 August 2024
Accepted: 23 August 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)