Vanishing theorems for \(L^{2}\) harmonic forms on complete Riemannian manifolds

DOI10.1007/s10711-016-0165-1zbMath1353.53047arXiv1407.0236OpenAlexW2344462384MaRDI QIDQ329350

Matheus Vieira

Publication date: 21 October 2016

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.0236

zbMATH Keywords

vanishing theoremsharmonic formsstable minimal hypersurfacesweighted Poincaré inequalities

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (14)

Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds ⋮ Harmonic \(p\)-forms on Hadamard manifolds with finite total curvature ⋮ Vanishing theorems for \(L^2\) harmonic \(p\)-forms on Riemannian manifolds with a weighted \(p\)-Poincaré inequality ⋮ A note on \(p\)-harmonic \(\ell\)-forms on complete non-compact manifolds ⋮ harmonic 1-forms on hypersurfaces with finite index ⋮ Unnamed Item ⋮ Vanishing theorems for Riemannian manifolds with nonnegative scalar curvature and weighted \(p\)-Poincaré inequality ⋮ Unnamed Item ⋮ \(L^2_f\)-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 ⋮ \(p\)-harmonic \(\ell\)-forms on Riemannian manifolds with a weighted Poincaré inequality ⋮ Harmonic 1-forms on immersed hypersurfaces in a Riemannian manifold with weighted bi-Ricci curvature bounded from below ⋮ Liouville-type theorems for weighted \(p\)-harmonic 1-forms and weighted \(p\)-harmonic maps ⋮ Vanishing theorems for complete Riemannian manifolds with nonnegative scalar curvature

Cites Work

• Unnamed Item
• Unnamed Item
• Refined Kato inequalities for harmonic fields on Kähler manifolds
• Vanishing theorems for \(L^2\) harmonic 1-forms on complete submanifolds in a Riemannian manifold
• Comparison theorem for Kähler manifolds and positivity of spectrum
• The structure of weakly stable constant mean curvature hypersurfaces
• One end theorem and application to stable minimal hypersurfaces
• Stability of minimal hypersurfaces
• Harmonic functions and the structure of complete manifolds
• \(L^ 2\) harmonic forms and stability of minimal hypersurfaces
• The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Refined Kato inequalities and conformal weights in Riemannian geometry
• Complete manifolds with positive spectrum
• Complete manifolds with positive spectrum. II.
• On stable minimal surfaces in manifolds of positive bi-Ricci curvatures
• On the structure of complete hypersurfaces in a Riemannian manifold of nonnegative curvature and \(L^2\) harmonic forms
• Spectrum of the Laplacian on quaternionic Kähler manifolds
• Results on a weighted Poincaré inequality of complete manifolds
• STABLE MINIMAL HYPERSURFACES IN THE HYPERBOLIC SPACE
• Eigenvalue estimates for minimal surfaces in hyperbolic space
• Weighted Poincaré inequality and rigidity of complete manifolds
• Connectedness at infinity of complete Kähler manifolds
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Stable minimal hypersurfaces in a nonnegatively curved manifold
• L 2 harmonic forms and stability of hypersurfaces with constant mean curvature
• Geometric Analysis
• Eigenvalue estimates for submanifolds with bounded mean curvature in the hyperbolic space

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