Conformal Structures and Necksizes of Embedded Constant Mean Curvature Surfaces
| dc.creator | Kusner, Rob | |
| dc.date | 2002-07-19 | |
| dc.date.accessioned | 2026-07-07T04:49:44Z | |
| dc.date.available | 2026-07-07T04:49:44Z | |
| dc.description | Let M = M_{g,k} denote the space of properly (Alexandrov) embedded constant mean curvature (CMC) surfaces of genus g with k (labeled) ends, modulo rigid motions, endowed with the real analytic structure described in [kmp]. Let $P = P_{g,k} = r_{g,k} \times R_+^k$ be the space of parabolic structures over Riemann surfaces of genus g with k (marked) punctures, the real analytic structure coming from the 3g-3+k local complex analytic coordinates on the Riemann moduli space r_{g,k}. Then the parabolic classifying map, Phi: M --> P, which assigns to a CMC surface its induced conformal structure and asymptotic necksizes, is a proper, real analytic map. It follows that Phi is closed and in particular has closed image. For genus g=0, this can be used to show that every conformal type of multiply punctured Riemann sphere occurs as a CMC surface, and -- under a nondegeneracy hypothesis -- that Phi has a well defined (mod 2) degree. This degree vanishes, so generically an even number of CMC surfaces realize any given conformal structure and asymptotic necksizes. | |
| dc.description | 10 pages, 2 figures, 2001 MSRI/Clay workshop on global theory of minimal surfaces | |
| dc.identifier | https://arxiv.org/abs/math/0207160 | |
| dc.identifier | http://arxiv.org/abs/math/0207160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64540 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A10 | |
| dc.title | Conformal Structures and Necksizes of Embedded Constant Mean Curvature Surfaces | |
| dc.type | text |