The Yamabe problem for higher order curvatures
| dc.creator | Sheng, Weimin | |
| dc.creator | Trudinger, Neil S | |
| dc.creator | Wang, Xu-jia | |
| dc.date | 2005-05-23 | |
| dc.date.accessioned | 2026-07-07T05:20:09Z | |
| dc.date.available | 2026-07-07T05:20:09Z | |
| dc.description | Let M be a compact Riemannian manifold of dimension n. The k-curvature, for k=1,2,..n, is defined as the k-th elementary symmetric polynomial of the eigenvalues of the Schouten tenser. The k-Yamabe problem is to prove the existence of a conformal metric whose k-curvature is a constant. When k=1, it reduces to the well-known Yamabe problem. Under the assumption that the metric is admissible, the existence of solutions to the k-Yamabe problem was recently proved by Gursky and Viaclovsky for k>n/2. In this paper we prove the existence of solutions for the remaining cases k <n/2, k=n/2, assuming that the equation is variational. | |
| dc.identifier | https://arxiv.org/abs/math/0505463 | |
| dc.identifier | http://arxiv.org/abs/math/0505463 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75272 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53C20;35J60,35K55 | |
| dc.title | The Yamabe problem for higher order curvatures | |
| dc.type | text |