The lower bound of the Ricci curvature that yields an infinite discrete spectrum of the Laplacian

DOI10.5802/aif.2651zbMath1252.58017arXiv0902.1919OpenAlexW2329023690MaRDI QIDQ407798

Hironori Kumura

Publication date: 28 March 2012

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.1919

zbMATH Keywords

Ricci curvatureLaplace-Beltrami operatordiscrete spectrum

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Growth of the eigensolutions of Laplacians on Riemannian manifolds. II: Positivity of the initial energy ⋮ On some aspects of oscillation theory and geometry

Cites Work

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• Geometric relative Hardy inequalities and the discrete spectrum of Schrödinger operators on manifolds
• Function theory on manifolds which possess a pole
• Corrections to the classical behavior of the number of bound states of Schrödinger operators
• A relation between growth and the spectrum of the Laplacian
• On the essential spectrum of a complete Riemannian manifold
• Eigenvalue comparison theorems and its geometric applications
• Partial differential equations. 2: Qualitative studies of linear equations

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