The Scalar Curvature Deformation Equation on Locally Conformally Flat Manifolds
| dc.creator | Yan, Yu | |
| dc.date | 2007-03-20 | |
| dc.date.accessioned | 2026-07-07T07:52:51Z | |
| dc.date.available | 2026-07-07T07:52:51Z | |
| dc.description | We study the equation $Δ_g u -\frac{n-2}{4(n-1)}R(g)u+Ku^p=0 (1+ζ\leq p \leq \frac{n+2}{n-2})$ on locally conformally flat compact manifolds $(M^n,g)$. We prove the following: (i) When the scalar curvature $R(g)>0$ and the dimension $n \geq 4$, under suitable conditions on $K$, all positive solutions $u$ have uniform upper and lower bounds; (ii) When the scalar curvature $R(g)\equiv 0$ and $n \geq 5$, under suitable conditions on $K$, all positive solutions $u$ with bounded energy have uniform upper and lower bounds. We also give an example to show that the energy bound condition for the uniform estimates in math.DG/0602636 is necessary. | |
| dc.identifier | https://arxiv.org/abs/math/0703563 | |
| dc.identifier | http://arxiv.org/abs/math/0703563 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126033 | |
| dc.subject | Differential Geometry | |
| dc.title | The Scalar Curvature Deformation Equation on Locally Conformally Flat Manifolds | |
| dc.type | text |