On Harnack inequalities and singularities of admissible metrics in the Yamabe problem
| dc.creator | Trudinger, Neil S. | |
| dc.creator | Wang, Xu-Jia | |
| dc.date | 2005-09-15 | |
| dc.date.accessioned | 2026-07-07T05:23:13Z | |
| dc.date.available | 2026-07-07T05:23:13Z | |
| dc.description | In this paper we study the local behaviour of admissible metrics in the k-Yamabe problem on compact Riemannian manifolds $(M, g_0)$ of dimension $n\ge 3$. For $n/2 <k<n$, we prove a sharp Harnack inequality for admissible metrics when $(M,g_0)$ is not conformally equivalent to the unit sphere $S^n$ and that the set of all such metrics is compact. When $(M,g_0)$ is the unit sphere we prove there is a unique admissible metric with singularity. As a consequence we prove an existence theorem for equations of Yamabe type, thereby recovering a recent result of Gursky and Viaclovski on the solvability of the $k$-Yamabe problem for $k>n/2$. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0509341 | |
| dc.identifier | http://arxiv.org/abs/math/0509341 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76352 | |
| dc.subject | Differential Geometry | |
| dc.title | On Harnack inequalities and singularities of admissible metrics in the Yamabe problem | |
| dc.type | text |