Torres de sela Scherk com gênero par arbitrário em R^3
Hancco, Alvaro Julio Yucra
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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 [16, 17]). In the singly periodic case, Karcher s examples of positive genera had been unique until Traizet obtained new ones in 1996 (see ). 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 Martin and Ramos Batista (see ), all of them with genus one. For genus two, the first such towers were constructed in 2010 (see ). Back to 2009, implicit towers of arbitrary genera were found in . In our present work we obtain explicit minimal Scherk saddle towers, for any given genus 2k, k ≥ 3, that we denote ST2k. We also present the MATLAB and Evolver programming that make it possible to generate the surfaces ST2k. MATLAB is an abbreviation forMatrix Laboratory, a program developed and distributed by MathWorks. Evolver is a free iterative program developed by Kenneth A. Brakke, a professor at Susquehanna University (see [3, 34]).