Conformally flat manifolds, Kleinian groups and scalar curvature

1988 ◽  
Vol 92 (1) ◽  
pp. 47-71 ◽  
Author(s):  
R. Schoen ◽  
S. -T. Yau
Keyword(s):  
Scalar Curvature ◽  
Kleinian Groups ◽  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Flat Manifolds

scholarly journals SOME COMPACTNESS RESULTS RELATED TO SCALAR CURVATURE DEFORMATION

2007 ◽  
Vol 09 (01) ◽  
pp. 81-120 ◽  
Author(s):  
YU YAN
Keyword(s):  
Scalar Curvature ◽  
Lower Bounds ◽  
Blow Up ◽  
Upper And Lower Bounds ◽  
Conformally Flat ◽  
Conformally Flat Manifolds ◽  
Locally Conformally Flat ◽  
Curvature Deformation ◽  
Flat Manifolds ◽  
Curvature Problem

Motivated by the prescribing scalar curvature problem, we study the equation [Formula: see text] on locally conformally flat manifolds (M,g) with R(g) ≡ 0. We prove that when K satisfies certain conditions and the dimension of M is 3 or 4, any positive solution u of this equation with bounded energy has uniform upper and lower bounds. Similar techniques can also be applied to prove that on four-dimensional locally conformally flat scalar positive manifolds the solutions of [Formula: see text] can only have simple blow-up points.

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