| Full text | |
| Author(s): |
Total Authors: 2
|
| Affiliation: | [1] Univ Sao Paulo, IME, BR-09500900 Sao Paulo - Brazil
[2] Univ Liverpool, Dept Math Sci, Liverpool L69 3BX, Merseyside - England
Total Affiliations: 2
|
| Document type: | Journal article |
| Source: | PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA; v. 107, n. 32, p. 14030-14035, AUG 10 2010. |
| Web of Science Citations: | 1 |
| Abstract | |
It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed. (AU) | |
| FAPESP's process: | 06/03829-2 - Dynamic in low dimensions |
| Grantee: | André Salles de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |