Extrema of curvature functionals on the space of metrics on 3-manifolds, II
| dc.creator | Anderson, Michael T. | |
| dc.date | 1999-12-21 | |
| dc.date.accessioned | 2026-07-07T06:33:01Z | |
| dc.date.available | 2026-07-07T06:33:01Z | |
| dc.description | Several rigidity results are proved for critical points of natural Riemannian functionals on the space of metrics on 3-manifolds. Two of these results are as follows. Let (N, g) be a complete Riemannian 3-manifold, satisfying one of the following variational conditions: (i) (N, g) has non-negative scalar curvature and is a critical point for the L^2 norm of the full curvature R among compact perturbations of (N, g). (ii) (N, g) has non-negative scalar curvature, a free isometric S^1 action, and is a critical point of the L^2 norm of R among compact volume non-increasing perturbations of (N, g) with non-negative scalar curvature. In either case, (N, g) is flat. The Schwarzschild metric (on the space-like hypersurface) has an isometric S^1 action and satisfies the other assumptions in (ii), showing that this result is sharp. | |
| dc.description | 45 pages, no figures. to appear in Calc.Var.&P.D.E | |
| dc.identifier | https://arxiv.org/abs/math/9912177 | |
| dc.identifier | http://arxiv.org/abs/math/9912177 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99058 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58E11 58J60 | |
| dc.title | Extrema of curvature functionals on the space of metrics on 3-manifolds, II | |
| dc.type | text |