scholarly journals Convex-cocompactness of Kleinian groups and conformally flat manifolds with positive scalar curvature

2002 ◽  
Vol 130 (12) ◽  
pp. 3731-3740 ◽  
Author(s):  
Hiroyasu Izeki
2007 ◽  
Vol 09 (01) ◽  
pp. 81-120 ◽  
Author(s):  
YU YAN

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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