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arXiv · 2201.06375

Eigenvalue estimates on weighted manifolds

Volker Branding·Georges Habib
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Abstract

We derive various eigenvalue estimates for the Hodge Laplacian acting on differential forms on weighted Riemannian manifolds. Our estimates unify and extend various results from the literature and we provide a number of geometric applications. In particular, we derive an inequality which relates the eigenvalues of the Jacobi operator for (f)-minimal hypersurfaces and the spectrum of the Hodge Laplacian.

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Volker Branding, Georges Habib. 2022-01-17. Eigenvalue estimates on weighted manifolds. https://doi.org/10.1007/s00025-024-02214-3

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