A new proof of the classification of solutions to some linearized fractional Yamabe type equations

The classifications of all the solutions to the linearized Yamabe equations and fractional Yamabe type equations are crucial to the proof of the compactness of the scalar curvature problems and the fractional scalar curvature problems respectively. These classifications, though having been proved in an analytical way before, have been proved by adopting some new geometric approaches from the perspective of conformal geometry.