We give a simple, direct proof of the easy fact about the Weierstrass Representation, namely, that it always gives a minimal surface. Most presentations include the much harder converse that every simply connected minimal surface is given by the Weierstrass Representation.
Professor Frank Morgan, Atwell Professor of Mathematics, Williams College
"The Weierstrass representation always gives a minimal surface,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 14
, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol14/iss1/4