Explicit minimal scherk saddle towers of arbitrary even genera in R3
| Autor: | A. J. Yucra Hancco, G. A. Lobos, V. Ramos Batista |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Recercat. Dipósit de la Recerca de Catalunya instname Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Publicacions Matemàtiques; Vol. 58, Núm. 2 (2014); p. 445-468 |
| Popis: | Starting from works by Scherk (1835) and by Enneper-Weierstrass (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see [9, 10]). In the singly periodic case, Karcher's examples of positive genera had been unique until Traizet obtained new ones in 1996 (see [23]). However, Traizet's construction is implicit and excludes towers, namely the desingularisation of more than two concurrent planes. Then, new explicit towers were found only in 2006 by Martín and Ramos Batista (see [13]), all of them with genus one. For genus two, the first such towers were constructed in 2010 (see [22]). Back to 2009, implicit towers of arbitrary genera were found in [5]. In our present work we obtain explicit minimal Scherk saddle towers, for any given genus 2k, k 3. |
| Databáze: | OpenAIRE |
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