2016/02/03 by Galimberti, Luca
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1602.01357
Given a compact and connected four dimensional smooth Riemannian manifold (M,g0) with kP := ∫M Qg0 dVg0 <0 and a smooth non-constant function f0 with maxp∈ Mf0(p)=0, all of whose maximum points are non-degenerate, we assume that the Paneitz operator is nonnegative and with kernel consisting of constants. Then, we are able to prove that for sufficiently small λ>0 there are at least two distinct conformal metrics gλ=e2uλg0 and gλ=e2uλg0 of Q-curvature Qgλ=Qgλ=f0+λ. Moreover, by means of the "monotonicity trick", we obtain crucial estimates for the "large" solutions uλ which enable us to study their "bubbling behavior" as λ\downarrow 0.