On a geometric equation with critical nonlinearity on the boundary
| dc.creator | Felli, Veronica | |
| dc.creator | Ahmedou, Mohameden Ould | |
| dc.date | 2001-06-26 | |
| dc.date | 2002-05-22 | |
| dc.date.accessioned | 2026-07-07T04:42:19Z | |
| dc.date.available | 2026-07-07T04:42:19Z | |
| dc.description | A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a $C^2$ function $H$ to be the mean curvature of some conformal flat metric is that $H$ is positive somewhere. We show that, when the boundary is umbilic and the function $H$ is positive everywhere, all such metrics stay in a compact set with respect to the $C^2$ norm and the total degree of all solutions is equal to -1. | |
| dc.description | 28 pages | |
| dc.identifier | https://arxiv.org/abs/math/0106219 | |
| dc.identifier | http://arxiv.org/abs/math/0106219 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61732 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Differential Geometry | |
| dc.subject | 35J60, 53C21, 58G30 | |
| dc.title | On a geometric equation with critical nonlinearity on the boundary | |
| dc.type | text |