Upper bounds for the second nonzero eigenvalue of the Laplacian via folding and conformal volume

Mehdi Eddaoudi; Alexandre Girouard

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arXiv · 2501.08761

Upper bounds for the second nonzero eigenvalue of the Laplacian via folding and conformal volume

Mehdi Eddaoudi·Alexandre Girouard

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Abstract

We prove an upper bound for the volume-normalized second nonzero eigenvalue of the Laplace operator on closed Riemannian manifold, in terms of the conformal volume. This bound provides effective upper bound for a large class of manifolds, thereby generalizing many known results.

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Mehdi Eddaoudi, Alexandre Girouard. 2025-01-15. Upper bounds for the second nonzero eigenvalue of the Laplacian via folding and conformal volume. https://arxiv.org/abs/2501.08761

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