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<p>Let (Ω<sup><i>n</i>+1</sup>, <i>g</i>) be an (<i>n</i>+1)-dimensional smooth compact connected Riemannian manifold with smooth boundary ∂Ω = Σ. Assume that the Ricci curvature of Ω is nonnegative and the principal curvatures of Σ are bounded from below by a positive constant <i>c</i>. In this paper, by constructing a new weight function, the authors obtain a lower bound of the first nonzero Steklov eigenvalue under the assumption that Sec<sub>Ω</sub> ≥ −<i>k</i>, where <i>k</i> is a positive constant. The authors also extend this result to the Steklov-type eigenvalue problem of the weighted Laplacian on a metric measure space.</p>

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Lower Bound Estimates of the First Steklov Eigenvalue for Compact Manifolds

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Yiwei Liu,
  • Yi-hu Yang

摘要

Let (Ωn+1, g) be an (n+1)-dimensional smooth compact connected Riemannian manifold with smooth boundary ∂Ω = Σ. Assume that the Ricci curvature of Ω is nonnegative and the principal curvatures of Σ are bounded from below by a positive constant c. In this paper, by constructing a new weight function, the authors obtain a lower bound of the first nonzero Steklov eigenvalue under the assumption that SecΩ ≥ −k, where k is a positive constant. The authors also extend this result to the Steklov-type eigenvalue problem of the weighted Laplacian on a metric measure space.