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<p>In this paper, we first give some lower bound estimate for the first eigenvalues of buckling and clamped plate problems on a complete non-compact submanifold in a strong negatively curved space, under an integral pinching condition on the mean curvature. Secondly, we establish lower bounds for these eigenvalue problems on bounded domains of a Riemannian manifold with Ricci curvature bounded from below by a negative constant, in terms of the inradius and the mean curvature of its boundary.</p>

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Lower bounds for the first eigenvalues of the biharmonic operators on Riemannian (sub)manifolds

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Hezi Lin

摘要

In this paper, we first give some lower bound estimate for the first eigenvalues of buckling and clamped plate problems on a complete non-compact submanifold in a strong negatively curved space, under an integral pinching condition on the mean curvature. Secondly, we establish lower bounds for these eigenvalue problems on bounded domains of a Riemannian manifold with Ricci curvature bounded from below by a negative constant, in terms of the inradius and the mean curvature of its boundary.