Covariant Schrödinger operator and \(L^2\)-vanishing property on Riemannian manifolds

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Elliptic equations on manifolds, general theory (58J05) Rigidity results (53C24) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

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Vanishing theorems for \(L^{2}\) harmonic forms on complete Riemannian manifolds
\(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality
Harmonic forms on manifolds with weighted Poincaré inequality
Vanishing theorems for square-integrable harmonic forms
Harmonic functions and the structure of complete manifolds
\(L^2\)-cohomology and Sobolev inequalities
Complete manifolds with positive spectrum
Covariant Schrödinger semigroups on Riemannian manifolds
Partial differential equations. 2: Qualitative studies of linear equations
\(L^2_f\)-harmonic \(1\)-forms on smooth metric measure spaces with positive \(\lambda_1(\Delta_f)\)
Vanishing theorems for \(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality
Vanishing theorems for \(L^2\) harmonic \(p\)-forms on Riemannian manifolds with a weighted \(p\)-Poincaré inequality
Vanishing theorems for Riemannian manifolds with nonnegative scalar curvature and weighted \(p\)-Poincaré inequality
Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature
Vanishing theorems for \(f\)-harmonic forms on smooth metric measure spaces
Harmonic forms on manifolds with non-negative Bakry-Émery-Ricci curvature
Vanishing theorems for \(p\)-harmonic forms on Riemannian manifolds
Vanishing results from Lichnerowicz Laplacian on complete Kähler manifolds and applications
A note on \(p\)-harmonic \(\ell\)-forms on complete non-compact manifolds
Results on a weighted Poincaré inequality of complete manifolds
Manifolds with a weighted Poincaré inequality

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