Convex Combinations of Minimal Graphs

Abstract

Given a collection of minimal graphs, 𝑀1,𝑀2,…,𝑀𝑛, with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions on 𝑀1,𝑀2,…,𝑀𝑛 so that a convex combination of them will be a minimal graph. We will then provide two examples, taking a convex combination of Scherk's doubly periodic surface with the catenoid and Enneper's surface, respectively.