International Journal of Mathematics and Mathematical Sciences (Jan 2012)
Convex Combinations of Minimal Graphs
Abstract
Given a collection of minimal graphs, π1,π2,β¦,ππ, with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions on π1,π2,β¦,ππ 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.