Eigenvalue Estimates on Weighted Manifolds

Volker Branding, Georges Habib

Publications: Contribution to journalArticlePeer Reviewed

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 languageEnglish
Article number187
JournalResults in Mathematics
Volume79
Issue number5
DOIs
Publication statusPublished - Aug 2024

Austrian Fields of Science 2012

  • 101006 Differential geometry

Keywords

  • 35P15
  • 53C42
  • 58J50
  • eigenvalue estimates
  • Hodge Laplacian
  • Jacobi operator
  • weighted manifold

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