Remark about the spectrum of the 𝑝-form Laplacian under a collapse with curvature bounded below

DOI10.1090/S0002-9939-03-07121-1zbMath1042.58018arXivmath/0202196WikidataQ125391218 ScholiaQ125391218MaRDI QIDQ4441807

John Lott

Publication date: 7 January 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0202196

zbMATH Keywords

Riemannian manifoldspectrum of the Laplacian

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50)

Related Items (5)

Elliptic PDEs on Compact Ricci Limit Spaces and Applications ⋮ $p$-spectrum and collapsing of connected sums ⋮ Collapsing, spectrum, and Diophantine properties of Riemannian flows ⋮ The gap of the eigenvalues for \(p\)-forms and harmonic \(p\)-forms of constant length ⋮ A Cheeger-like inequality for coexact 1-forms

Cites Work

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• A note on the first nonzero eigenvalue of the Laplacian acting on p- forms
• Collapsing and pinching under a lower curvature bound
• The fundamental groups of almost nonnegatively curved manifolds
• Collapsing and the differential form Laplacian: the case of a smooth limit space.
• Small eigenvalues on \(p\)-forms for collapsings of the even-dimensional spheres
• From vanishing theorems to estimating theorems: the Bochner technique revisited
• A De Rham Type Theorem for Orbit Spaces
• Eigenvalues of the Laplacian on Forms

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