The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces
| dc.creator | Kusner, Rob | |
| dc.creator | Mazzeo, Rafe | |
| dc.creator | Pollack, Daniel | |
| dc.date | 1994-08-19 | |
| dc.date.accessioned | 2026-07-07T09:12:25Z | |
| dc.date.available | 2026-07-07T09:12:25Z | |
| dc.description | We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of all such surfaces with $k$ ends (where surfaces are identified if they differ by an isometry of $\RR^{3}$) is locally a real analytic variety. When the linearization of the quasilinear elliptic equation specifying mean curvature equal to one has no $L^2-$nullspace we prove that $\Mk$ is locally the quotient of a real analytic manifold of dimension $3k-6$ by a finite group (iė\. a real analytic orbifold), for $k\geq 3$. This finite group is the isotropy subgroup of the surface in the group of Euclidean motions. It is of interest to note that the dimension of $\Mk$ is independent of the topology of the underlying punctured Riemann surface to which $\Sig$ is conformally equivalent. These results also apply to hypersurfaces of $\HH^{n+1}$ with nonzero constant mean curvature greater than that of a horosphere and whose ends are cylindrically bounded. | |
| dc.description | 15 pages, amsTeX | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9408004 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9408004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152013 | |
| dc.subject | Differential Geometry | |
| dc.title | The Moduli Space of Complete Embedded Constant Mean Curvature Surfaces | |
| dc.type | text |