2023/02/05 by Mayer, Martin, Zhu, Chaona
#Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2302.02435
The problem of prescribing conformally the scalar curvature on a closed Riemannian manifold of negative Yamabe invariant is always solvable, when the function K to be prescribed is strictly negative, while sufficient and necessary conditions are known for K≤ 0. For sign changing K Rauzy showed solvability, if K is not too positive. We revisit this problem in a different variational context, thereby recovering and quantifying the principle existence result of Rauzy and show under additional assumptions, that for a sign changing K solutions to the conformally prescribed scalar curvature problem, while existing, are not unique.