Prescribing curvatures on three dimensional Riemannian manifolds with boundaries
| dc.creator | Zhang, Lei | |
| dc.date | 2008-10-28 | |
| dc.date.accessioned | 2026-07-07T10:13:38Z | |
| dc.date.available | 2026-07-07T10:13:38Z | |
| dc.description | Let $(M,g)$ be a complete three dimensional Riemannian manifold with boundary $\partial M$. Given smooth functions $K(x)>0$ and $c(x)$ defined on $M$ and $\partial M$, respectively, it is natural to ask whether there exist metrics conformal to $g$ so that under these new metrics, $K$ is the scalar curvature and $c$ is the boundary mean curvature. All such metrics can be described by a prescribing curvature equation with a boundary condition. With suitable assumptions on $K$,$c$ and $(M,g)$ we show that all the solutions of the equation can only blow up at finite points over each compact subset of $\bar M$, some of them may appear on $\partial M$. We describe the asymptotic behavior of the blowup solutions around each blowup point and derive an energy estimate as a consequence. | |
| dc.description | 21 pages. Transactions of American Mathematical Society, in press | |
| dc.identifier | https://arxiv.org/abs/0810.5027 | |
| dc.identifier | http://arxiv.org/abs/0810.5027 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172600 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J60, 53B20 | |
| dc.title | Prescribing curvatures on three dimensional Riemannian manifolds with boundaries | |
| dc.type | text |