A Note on Existence and Non-existence of Minimal Surfaces in Some Asymptotically Flat 3-manifolds
| dc.creator | Miao, Pengzi | |
| dc.date | 2006-01-19 | |
| dc.date.accessioned | 2026-07-07T09:50:46Z | |
| dc.date.available | 2026-07-07T09:50:46Z | |
| dc.description | Motivated by problems on apparent horizons in general relativity, we prove the following theorem on minimal surfaces: Let $g$ be a metric on the three-sphere $S^3$ satisfying $Ric(g) \geq 2 g$. If the volume of $(S^3, g)$ is no less than one half of the volume of the standard unit sphere, then there are no closed minimal surfaces in the asymptotically flat manifold $(S^3 \setminus \{P \}, G^4 g)$. Here $G$ is the Green's function of the conformal Laplacian of $(S^3, g)$ at an arbitrary point $P$. We also give an example of $(S^3, g)$ with $Ric(g) > 0$ where $(S^3 \setminus \{P \}, G^4 g)$ does have closed minimal surfaces. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601480 | |
| dc.identifier | http://arxiv.org/abs/math/0601480 | |
| dc.identifier | Math. Res. Lett. 14, no. 3, 395-402 (2007) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165055 | |
| dc.subject | Differential Geometry | |
| dc.subject | Mathematical Physics | |
| dc.title | A Note on Existence and Non-existence of Minimal Surfaces in Some Asymptotically Flat 3-manifolds | |
| dc.type | text |