The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many Sides
The classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number of line segments. In this paper, we explore extensions to boundary curves which in one sense or another are made up of infinitely many line segments, wi...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/350326 |
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| _version_ | 1849404127907414016 |
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| author | Gonzalo Riera Hernán Carrasco Rubén Preiss |
| author_facet | Gonzalo Riera Hernán Carrasco Rubén Preiss |
| author_sort | Gonzalo Riera |
| collection | DOAJ |
| description | The classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number of line segments. In this paper, we explore extensions to boundary curves which in one sense or another are made up of infinitely many line segments, with specific attention to the “infinite staircase” and to the Koch snowflake, for both of which we develop explicit formulas for the mapping function and explain how one can use standard mathematical software to generate corresponding graphics. We also discuss a number of open questions suggested
by these considerations, some of which are related to differentials on hyperelliptic surfaces of infinite genus. |
| format | Article |
| id | doaj-art-9904f1e2eec44dd6b1cfb9e074c519a0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9904f1e2eec44dd6b1cfb9e074c519a02025-08-20T03:37:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/350326350326The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many SidesGonzalo Riera0Hernán Carrasco1Rubén Preiss2Departamento de Matemáticas, Pontificia Universidad Católica de Chile, Avenue Vicuña Makenna 4860, 7820436 Macul, Santiago, ChileDepartamento de Matemáticas, Pontificia Universidad Católica de Chile, Avenue Vicuña Makenna 4860, 7820436 Macul, Santiago, ChileDepartamento de Matemáticas, Pontificia Universidad Católica de Chile, Avenue Vicuña Makenna 4860, 7820436 Macul, Santiago, ChileThe classical Schwarz-Christoffel formula gives conformal mappings of the upper half-plane onto domains whose boundaries consist of a finite number of line segments. In this paper, we explore extensions to boundary curves which in one sense or another are made up of infinitely many line segments, with specific attention to the “infinite staircase” and to the Koch snowflake, for both of which we develop explicit formulas for the mapping function and explain how one can use standard mathematical software to generate corresponding graphics. We also discuss a number of open questions suggested by these considerations, some of which are related to differentials on hyperelliptic surfaces of infinite genus.http://dx.doi.org/10.1155/2008/350326 |
| spellingShingle | Gonzalo Riera Hernán Carrasco Rubén Preiss The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many Sides International Journal of Mathematics and Mathematical Sciences |
| title | The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many Sides |
| title_full | The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many Sides |
| title_fullStr | The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many Sides |
| title_full_unstemmed | The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many Sides |
| title_short | The Schwarz-Christoffel Conformal Mapping for “Polygons” with Infinitely Many Sides |
| title_sort | schwarz christoffel conformal mapping for polygons with infinitely many sides |
| url | http://dx.doi.org/10.1155/2008/350326 |
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