Convex Combinations of Minimal Graphs

الملخص EN

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.