Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries
| dc.creator | Felli, Veronica | |
| dc.creator | Ahmedou, Mohameden Ould | |
| dc.date | 2001-04-03 | |
| dc.date.accessioned | 2026-07-07T04:40:58Z | |
| dc.date.available | 2026-07-07T04:40:58Z | |
| dc.description | This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean curvature on the boundary. By means of blow-up analysis techniques and the Positive Mass Theorem, we show that on locally conformally flat manifolds with umbilic boundary all metrics stay in a compact set with respect to the $C^2$-norm and the total Leray-Schauder degree of all solutions is equal to -1. Then we deduce from this compactness result the existence of at least one solution to our problem. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/math/0104041 | |
| dc.identifier | http://arxiv.org/abs/math/0104041 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61225 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J60; 53C21; 58G30 | |
| dc.title | Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries | |
| dc.type | text |