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

  • Yong LUO ,
  • Xianjing ZHENG
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  • Mathematical Science Research Center, Chongqing University of Technology, Chongqing 400054, China
Yong LUO, E-mail: yongluo-math@cqut.edu.cn

Received date: 2025-02-20

  Revised date: 2025-06-23

  Online published: 2026-05-22

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 $\mathbb{H}^n(-1)$.

Cite this article

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 . DOI: 10.1007/s10473-026-0210-6

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