Compactness of solutions to the Yamabe problem

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A priori estimates for the Yamabe problem in the non-locally conformally flat case (2004, background): “The author was just recently communicated that Li and Zhang ([ 9 ]) have independently proved the same compactness result.”
Blowup Solutions of Some Nonlinear Elliptic Equations Involving Exponential Nonlinearities (2006, methodology): “Similar ideas have been used in the author’s joint work with Li [13, 14] on the compactness of the solutions of the Yamabe equation.”
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres (2011, background): “It follows that the C2,α-a priori estimates proved by Li and Zhang [14,15] and Marques [16] hold for the metrics in [gtk ], which implies that the set { g ∈ [gt ], t ∈ {tk, k ∈ N} ∪ {t∗} : g ∈ Met1 ( S2n+1 ) , scal(g) = const.”