Complete conformal metrics of constant positive scalar curvature with prescribed isolated singularities
Year: 2026
Type: preprint
Abstract: Let $(M^n,g)$ be a smooth closed connected Riemannian manifold of dimension $n\ge3$ with positive Yamabe constant. For any prescribed finite set $Λ\subset M$ containing at least two points, we construct a complete metric on $M\setminusΛ$, conformal to $g$, with scalar curvature $n(n-1)$. At each singularity, the local geometric term in the reduced action comes from the first nonzero homogeneous metric term of degree at most $(n-2)/2$ in finite conformal normal coordinates, or from the mass of the Green function metric when all such terms vanish. We completely solve Schoen's conjecture about singular Yamabe problem.
Source: arXiv (Cornell University)
Authors: Chen, Hongyu, Ma, Li
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223294713