Positive mass theorem for the Yamabe problem on spin manifolds
| dc.creator | Ammann, Bernd | |
| dc.creator | Humbert, Emmanuel | |
| dc.date | 2003-04-03 | |
| dc.date | 2008-02-25 | |
| dc.date.accessioned | 2026-07-07T09:22:49Z | |
| dc.date.available | 2026-07-07T09:22:49Z | |
| dc.description | Let $(M,g)$ be a compact connected spin manifold of dimension $n\geq 3$ whose Yamabe invariant is positive. We assume that $(M,g)$ is locally conformally flat or that $n \in \{3,4,5\}$. According to a positive mass theorem of Witten, the constant term in the asymptotic development of the Green's function of the conformal Laplacian is positive if $(M,g)$ is not conformally equivalent to the sphere. In the present article, we will give a proof for this fact which is considerably shorter than previous proofs. Our proof is a modification of Witten's argument, but no analysis on asymtotically flat spaces is needed. | |
| dc.description | A term is missing in Version 2 and the printed version. The term is added in Version 3 | |
| dc.identifier | https://arxiv.org/abs/math/0304043 | |
| dc.identifier | http://arxiv.org/abs/math/0304043 | |
| dc.identifier | GAFA 15 (2005), 567-576 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155508 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53C21; 58E11; 53C27 | |
| dc.title | Positive mass theorem for the Yamabe problem on spin manifolds | |
| dc.type | text |