Torres de sela Scherk com gênero par arbitrário em R^3

• Ano de defesa: 2014
• Autor(a) principal: Hancco, Alvaro Julio Yucra
• Orientador(a): Villagra, Guillermo Antonio Lobos
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• País: BR
• Palavras-chave em Português: Geometria diferencial; Riemann, Superfícies de; Superfícies mínimas; Scherk, Torres de sela
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/5834

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 [41]). 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 [24]), all of them with genus one. For genus two, the first such towers were constructed in 2010 (see [40]). Back to 2009, implicit towers of arbitrary genera were found in [11]. 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]).