Acta mathematica scientia,Series B ›› 2026, Vol. 46 ›› Issue (2): 714-729.doi: 10.1007/s10473-026-0210-6

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UNIVERSAL INEQUALITIES FOR EIGENVALUES OF THE DIRICHLET LAPLACIAN ON CONFORMALLY FLAT RIEMANNIAN MANIFOLDS

Yong LUO, Xianjing ZHENG*   

  1. Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China
  • Received:2025-02-20 Revised:2025-06-23 Published:2026-05-22
  • Contact: *Xianjing ZHENG, E-mail: 1311169535@qq.com
  • About author:Yong LUO, E-mail: yongluo-math@cqut.edu.cn
  • Supported by:
    Luo's research was supported by the Natural Science Foundation of China (12271069), the Chongqing NSF (CSTB2024NSCQ-LZX0093) and the Municipal Education Chongqing Commission Humanities and Social Science Research Project (22SKSZ057).

Abstract: In this paper we study eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds. In particular we establish some universal inequality for eigenvalues of the Dirichlet Laplacian on the hyperbolic space $\mathbb{H}^n(-1)$.

Key words: eigenvalue, universal inequality, Laplacian, the hyperbolic space

CLC Number: 

  • 58J50
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