Bounded Outdegree and Extremal Length on Discrete Riemann Surfaces
| Autor: | Wood, William E. |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Conform. Geom. Dyn. 14 (2010), 194-201 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/S1088-4173-2010-00210-9 |
| Popis: | Let $T$ be a triangulation of a Riemann surface. We show that the 1-skeleton of $T$ may be oriented so that there is a global bound on the outdegree of the vertices. Our application is to construct extremal metrics on triangulations formed from $T$ by attaching new edges and vertices and subdividing its faces. Such refinements provide a mechanism of convergence of the discrete triangulation to the classical surface. We will prove a bound on the distortion of the discrete extremal lengths of path families on $T$ under the refinement process. Our bound will depend only on the refinement and not on $T$. In particular, the result does not require bounded degree. Comment: 9 pages, 2 figures |
| Databáze: | arXiv |
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