A representação de Weierstrass e os exemplos clássicos

Abstract

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.