Scherk saddle towers of genus two in R3

• Grant number: 10/11833-5
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2011
• End date: December 31, 2011
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Valério Ramos Batista
• Grantee: Bruno Henrique Torres
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

The project is based upon the article ``Scherk Saddle Towers of Genus Two in R3'', which shows the first examples of complete embedded minimal surfaces in R3 containing Gaussian geodesics. It also answers a 14-year conjecture: the embedding in R3 of the surfaces CSSCFF and CSSCCC from Callahan-Hoffman-Meeks-Wohlgemuth. The article is very rich in Geometric arguments, with proofs hinted by MatLab. This will teach the student how to make use of software to assure formal and original results. (AU)