A representação de Weierstrass e os exemplos clássicos - Sampaio, Pedro Valim (Universidade Federal de São Carlos, 2026)
In this dissertation, we present an introduction to minimal surfaces in three-dimensional Euclidean space. After reviewing differentiable manifolds and isometric immersions, we study the Weierstrass representation, which allows minimal surfaces to be constructed from holomorphic and meromorphic functions. As examples, we discuss the catenoid, the helicoid, and Scherk’s surface, aiming to provide a clear, rigorous, and accessible exposition.
The Weierstrass representation and classical examples
Keywords: Superfícies mínimas; Imersões isométricas; Representação de Weierstrass; Geometria diferencial; Catenoide; Helicoide; Minimal surfaces; Isometric immersions; Weierstrass representation; Differential geometry; Catenoid; Helicoid; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIAL; 4. Educação de Qualidade