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arXiv · 2607.21959

Spectral bounds for $f$-Laplace-type operators with applications to Betti numbers on gradient Ricci shrinkers

Fei He
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Abstract

We study the spectrum of the $f$-Laplacian on complete gradient Ricci shrinkers. Upper and lower bounds for the $k$-th eigenvalue are established in terms of the volume growth rate. Both bounds are shown to be sharp in the exponent. The method extends to $f$-Laplace-type operators on vector bundles; as an application we obtain explicit upper bounds for the Betti numbers.

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Fei He. 2026-07-24. Spectral bounds for $f$-Laplace-type operators with applications to Betti numbers on gradient Ricci shrinkers. https://arxiv.org/abs/2607.21959

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