Fun\c{c}\~oes el\'iticas

TL;DR

This paper presents Karcher's geometric approach to elliptic functions and explores their applications in minimal surface theory, offering a more intuitive understanding and broader utility.

Contribution

It introduces Karcher's geometric formulation of elliptic functions and demonstrates their application in minimal surface problems, enhancing analytical control.

Findings

Karcher's approach provides better control over elliptic functions.

Application to minimal surfaces demonstrates practical utility.

Enhanced understanding of elliptic functions' behavior.

Abstract

In 1989 H.Karcher rewrote the theory of elliptic functions through an approach that is much more geometrical than analytical. Therewith he obtained an optimal control over the behaviour and image values of these functions, which allowed for their broad application in minimal surfaces. Our work is devoted to presenting the theory of elliptic functions according to Karcher's approach, as well as some of its applications in minimal surfaces. The original publication was a mini-course that can be downloaded at https://www.dm.ufscar.br/profs/lobos/IIEPG