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 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.
Original language | English |
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Article number | 187 |
Journal | Results in Mathematics |
Volume | 79 |
Issue number | 5 |
DOIs | |
Publication status | Published - Aug 2024 |
Austrian Fields of Science 2012
- 101006 Differential geometry
Keywords
- 35P15
- 53C42
- 58J50
- eigenvalue estimates
- Hodge Laplacian
- Jacobi operator
- weighted manifold