On the \(L^2\)-cohomology of a convex cocompact hyperbolic manifold

DOI10.1215/S0012-7094-02-11523-3zbMath1221.58023arXivmath/0210163OpenAlexW1980883970WikidataQ125600412 ScholiaQ125600412MaRDI QIDQ1395928

Xiaodong Wang

Publication date: 29 June 2003

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210163

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20) Hodge theory in global analysis (58A14) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)

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Vanishing properties of $p$-harmonic $\ell$-forms on Riemannian manifolds ⋮ Vanishing Theorems for Conformally Compact Manifolds ⋮ On 𝐿² cohomology of ACH Kähler manifolds ⋮ \(L^{p}\) harmonic 1-forms on submanifolds in spheres ⋮ Unnamed Item ⋮ Finiteness of non-parabolic ends on submanifolds in spheres ⋮ \(L^{2}\) harmonic 2-forms on minimal hypersurfaces in spheres ⋮ Harmonic 1-forms on minimal hypersurfaces in \(\mathbb{S}^n \times \mathbb{R}\) ⋮ Vanishing theorems on hypersurfaces in Riemannian manifolds ⋮ \(L ^{2}\)-harmonic forms and stable hypersurfaces in space forms ⋮ On the reduced \(L^2\) cohomology on complete hypersurfaces in Euclidean spaces ⋮ Rigidity of complete minimal hypersurfaces in the Euclidean space ⋮ \(L^{2}\) harmonic 1-forms on minimal submanifolds in spheres ⋮ A gap theorem on submanifolds with finite total curvature in spheres ⋮ Hypersurfaces in spheres with finite total curvature ⋮ Rigidity and \(L^2\) cohomology of hyperbolic manifolds ⋮ Bayesian Analysis of Curves Shape Variation Through Registration and Regression ⋮ \(L^p\) harmonic 1-forms on conformally flat Riemannian manifolds ⋮ Gap theorems on hypersurfaces in spheres

Cites Work

• Hodge theory on hyperbolic manifolds
• The Hodge cohomology of a conformally compact metric
• Conformally flat manifolds, Kleinian groups and scalar curvature
• Patterson-Sullivan measure and conformally flat metrics
• Rigidity for quasi-Möbius group actions
• Refined Kato inequalities and conformal weights in Riemannian geometry
• Kato constants in Riemannian geometry
• Invariant currents on limit sets
• On conformally compact Einstein manifolds.
• Related aspects of positivity in Riemannian geometry
• The spectrum of an asymptotically hyperbolic Einstein manifold
• Limit sets of Kleinian groups and conformally flat Riemannian manifolds
• The Boundary of Negatively Curved Groups

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