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<p>In this paper, we study the buckling problem of the drifting Laplacian on bounded domains in a complete Riemannian manifold whose corresponding smooth metric measure space has a nonnegative <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-dimensional Bakry-Émery Ricci curvature, and then establish some universal inequalities. In particular, our results can reveal the relationship between the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((k+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-th eigenvalue and the first <i>k</i> eigenvalues relatively quickly, and some methods used in this paper might be applied to other eigenvalue problems.</p>

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Inequalities for Eigenvalues of the Buckling Problem of the Drifting Laplacian

  • 期刊论文

  • 发表日期：

    2025年11月14日

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  • Yue He,
  • Jinglin Gong

摘要

In this paper, we study the buckling problem of the drifting Laplacian on bounded domains in a complete Riemannian manifold whose corresponding smooth metric measure space has a nonnegative \(\infty \) ∞ -dimensional Bakry-Émery Ricci curvature, and then establish some universal inequalities. In particular, our results can reveal the relationship between the \((k+1)\) ( k + 1 ) -th eigenvalue and the first k eigenvalues relatively quickly, and some methods used in this paper might be applied to other eigenvalue problems.