2019/09/07 by Andrea Malchiodi, Martin Mayer, Malchiodi, Andrea +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations
paper · doi:10.48550/arxiv.1909.03190
openalex publication_date 2019/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension n ≥ 5. We prove new existence results using Morse theory and some analysis on blowing-up solutions, under suitable pinching conditions on the curvature function. We also provide new non-existence results showing the sharpness of some of our assumptions, both in terms of the dimension and of the Morse structure of the prescribed function.