Some Compactness Results Related to Scalar Curvature Deformation
| dc.creator | Yan, Yu | |
| dc.date | 2006-02-27 | |
| dc.date | 2006-03-01 | |
| dc.date.accessioned | 2026-07-07T07:03:51Z | |
| dc.date.available | 2026-07-07T07:03:51Z | |
| dc.description | Motivated by the prescribing scalar curvature problem, we study the equation $Δ_g u +Ku^p=0 (1+ζ\leq p \leq \frac{n+2}{n-2})$ on locally conformally flat manifolds $(M,g)$ with $R(g)=0$. We prove that when $K$ satisfies certain conditions and the dimension of $M$ is 3 or 4, any solution $u$ of this equation with bounded energy has uniform upper and lower bounds. Similar techniques can also be applied to prove that on 4-dimensional scalar positive manifolds the solutions of $Δ_gu-\frac{n-2}{4(n-1)}R(g)u+Ku^p=0, K>0, 1+ζ\leq p \leq \frac{n+2}{n-2}$ can only have simple blow-up points. | |
| dc.identifier | https://arxiv.org/abs/math/0602636 | |
| dc.identifier | http://arxiv.org/abs/math/0602636 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/109136 | |
| dc.subject | Differential Geometry | |
| dc.title | Some Compactness Results Related to Scalar Curvature Deformation | |
| dc.type | text |