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

doi:10.1007/s10473-026-0210-6

数学物理学报(英文版) ›› 2026, Vol. 46 ›› Issue (2): 714-729.doi: 10.1007/s10473-026-0210-6

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

Yong LUO, Xianjing ZHENG^*

Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China

收稿日期:2025-02-20 修回日期:2025-06-23 发布日期:2026-05-22

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

Yong LUO, Xianjing ZHENG^*

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).

摘要/Abstract

摘要： 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 $\mathbb{H}^n(-1)$.

关键词: eigenvalue, universal inequality, Laplacian, the hyperbolic space

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

中图分类号:

58J50

Yong LUO, Xianjing ZHENG. UNIVERSAL INEQUALITIES FOR EIGENVALUES OF THE DIRICHLET LAPLACIAN ON CONFORMALLY FLAT RIEMANNIAN MANIFOLDS[J]. 数学物理学报(英文版), 2026, 46(2): 714-729.

Yong LUO, Xianjing ZHENG. UNIVERSAL INEQUALITIES FOR EIGENVALUES OF THE DIRICHLET LAPLACIAN ON CONFORMALLY FLAT RIEMANNIAN MANIFOLDS[J]. Acta mathematica scientia,Series B, 2026, 46(2): 714-729.

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

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

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