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Explicit minimal scherk saddle towers of arbitrary even genera in R3
Yucra Hancco, A. J. (DM. UFSCar (Sao Carlos, Brasil))
Lobos, G. A. (DM. UFSCar (Sao Carlos, Brasil))
Ramos Batista, V. (CMCC. UFABC (Santo André, Brasil))

Data: 2014
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Minimal ; Surfaces
Publicat a: Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 445-468, ISSN 0214-1493

Adreça original:
DOI: 10.5565/PUBLMAT_58214_22
DOI: 10.5565/287185

24 p, 613.2 KB

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