Nonexistence of complete conformal metrics with prescribed scalar curvatures on a manifold of nonpositive curvature

DOI10.1016/j.jmaa.2004.03.003zbMath1057.53025OpenAlexW2070837384MaRDI QIDQ596795

Zong Ben Xu, Zonglao Zhang

Publication date: 10 August 2004

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.03.003

zbMATH Keywords

Scalar curvatureComplete Riemannian manifoldConformal deformationPartial differential equation

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (2)

Entire radially symmetric graphs with prescribed mean curvature in warped product spaces ⋮ Notes on submanifolds in warped products

Cites Work

• Function theory on manifolds which possess a pole
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Conformal deformations of complete manifolds with negative curvature
• Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds
• On the elliptic equation \(\Delta \omega + K(x)e^{2\omega} = 0\) and conformal metrics with prescribed Gaussian curvatures
• Conformal deformations on a noncompact Riemannian manifold
• On conformal deformation of nonpositive curvature on noncompact surfaces
• Prescribing Scalar Curvatures on the Conformal Classes of Complete Metrics with Negative Curvature
• Conformal scalar curvature equations on complete manifolds
• On the elliptic equation Δ𝑢+𝑘𝑢-𝐾𝑢^{𝑝}=0 on complete Riemannian manifolds and their geometric applications
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