scholarly journals Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds

1988 ◽  
Vol 27 (2) ◽  
pp. 225-239 ◽  
Author(s):  
Patricio Aviles ◽  
Robert C. McOwen
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Conformal Deformation ◽  
Noncompact Riemannian Manifolds

scholarly journals Nonexistence for hyperbolic problems on Riemannian manifolds1

2020 ◽  
Vol 120 (1-2) ◽  
pp. 87-101
Author(s):  
Dario D. Monticelli ◽  
Fabio Punzo ◽  
Marco Squassina
Keyword(s):  
Euclidean Space ◽  
Riemannian Manifolds ◽  
Wave Operator ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Hyperbolic Problems ◽  
Power Nonlinearity ◽  
General Weight ◽  
Noncompact Riemannian Manifolds ◽  
General Weight Function

We establish necessary conditions for the existence of solutions to a class of semilinear hyperbolic problems defined on complete noncompact Riemannian manifolds, extending some nonexistence results for the wave operator with power nonlinearity on the whole Euclidean space. A general weight function depending on spacetime is allowed in front of the power nonlinearity.

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