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<p>Given a complete Riemannian <i>n</i>-manifold with sectional curvature bounded between two positive constants, the Dirichlet eigenvalue problem on a domain in this manifold is investigated. The gaps between consecutive eigenvalues are estimated to confirm the Chen–Zheng–Yang conjecture (Pac J Math 282(2):301–315, 2016) for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n \ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Gaps between consecutive Dirichlet eigenvalues for positively curved domains

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Laiyuan Gao,
  • Haoran Hou

摘要

Given a complete Riemannian n-manifold with sectional curvature bounded between two positive constants, the Dirichlet eigenvalue problem on a domain in this manifold is investigated. The gaps between consecutive eigenvalues are estimated to confirm the Chen–Zheng–Yang conjecture (Pac J Math 282(2):301–315, 2016) for \(n \ge 3\) n ≥ 3 .