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arXiv · 2608.26723

Extrinsic upper bounds for the harmonic mean of eigenvalues in curved manifolds

Hang Chen·Yuna Gao
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Abstract

Let $M$ be an $m (\ge2)$-dimensional closed orientable submanifold in a Riemannian manifold of sectional curvature bounded above by $\delta$. We obtain the extrinsic upper bounds of the harmonic mean of the first $m$ nonzero eigenvalues of the Laplacian on $M$, which extend the previous related results for the first nonzero eigenvalues.

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Hang Chen, Yuna Gao. 2026-08-27. Extrinsic upper bounds for the harmonic mean of eigenvalues in curved manifolds. https://arxiv.org/abs/2608.26723

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