On the Negative Case of the Singular Yamabe Problem
| dc.creator | Finn, David L. | |
| dc.date | 1996-01-16 | |
| dc.date.accessioned | 2026-07-07T09:12:41Z | |
| dc.date.available | 2026-07-07T09:12:41Z | |
| dc.description | The negative case of the Singular Yamabe Problem concerns the existence and behavior of complete metrics with constant negative scalar curvature on the complement of a closed set in a compact Riemannian manifold which are conformally equivalent to a smooth metric on this compact manifold. When the closed set is a smooth submanifold, it is known by the results of Loewner-Nirenberg and Aviles-McOwen that there exists such a complete metric if and only if $d > (n-2)/2$, and in general the Hausdorff dimension of the set must be at least $(n-2)/2$. In this paper, we show that the existence of such a complete conformal metric with constant negative scalar curvature depends on the tangent structure of the closed set. Specifically, provided the set has a nice tangent cone at a point, we show that when the dimension of this tangent cone is less than $(n-2)/2$ there can not exist such a negative Singular Yamabe metric. | |
| dc.description | 27 pages, Plain TeX | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9601006 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9601006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152105 | |
| dc.subject | Differential Geometry | |
| dc.title | On the Negative Case of the Singular Yamabe Problem | |
| dc.type | text |