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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb{H}^{n}(-1)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>.</p>

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Universal inequalities for eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年12月22日

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  • Yong Luo,
  • Xianjing Zheng

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 \(\mathbb{H}^{n}(-1)\) H n ( − 1 ) .