Scalar curvature and conformal deformations of noncompact Riemannian manifolds

1997 ◽  
Vol 225 (3) ◽  
pp. 395-426 ◽  
Author(s):  
Andrea Ratto ◽  
Marco Rigoli ◽  
Laurent Veron
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Conformal Deformations ◽  
Noncompact Riemannian Manifolds

On the conformal scalar curvature equations on Finsler manifolds

2016 ◽  
Vol 14 (01) ◽  
pp. 1750008
Author(s):  
Neda Shojaee ◽  
Morteza MirMohammad Rezaii
Keyword(s):  
Scalar Curvature ◽  
Finsler Geometry ◽  
Yamabe Problem ◽  
Finsler Manifolds ◽  
Yamabe Flow ◽  
Conformal Deformations

In this paper, we study conformal deformations and [Formula: see text]-conformal deformations of Ricci-directional and second type scalar curvatures on Finsler manifolds. Then we introduce the best equation to study the Yamabe problem on Finsler manifolds. Finally, we restrict conformal deformations of metrics to [Formula: see text]-conformal deformations and derive the Yamabe functional and the Yamabe flow in Finsler geometry.

On Capacitary Characteristics of Noncompact Riemannian Manifolds

2021 ◽  
Vol 65 (3) ◽  
pp. 61-67
Author(s):  
A. G. Losev ◽  
V. V. Filatov
Keyword(s):  
Riemannian Manifolds ◽  
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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