Minimal surfaces for undergraduates

TL;DR

This paper provides an accessible introduction to the theory of minimal surfaces in Euclidean spaces for undergraduates, using elementary calculus without requiring prior differential geometry knowledge.

Contribution

It offers an elementary, self-contained presentation of minimal surface theory suitable for second-year undergraduate students.

Findings

Introduces minimal surfaces using basic calculus concepts.

No advanced differential geometry needed for understanding.

Accessible to undergraduate students with standard analysis background.

Abstract

In this article we present an elementary introduction to the theory of minimal surfaces in Euclidean spaces $\mathbb R^n$ for $n\ge 3$ by using only elementary calculus of functions of several variables at the level of a typical second-year undergraduate analysis course for students of Mathematics at European universities. No prior knowledge of differential geometry is assumed.