Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2012, Article ID 724268, 9 pages doi:10.1155/2012/724268 Research Article Convex Combinations of Minimal Graphs Michael Dorff, 1 Ryan Viertel, 1 and Magdalena Woloszkiewicz 2 1 Department of Mathematics, Brigham Young University, Provo, UT 84602, USA 2 Department of Mathematics, Maria Curie-Sklodowska University, 20-031 Lublin, Poland Correspondence should be addressed to Michael Dorff, mdorff@math.byu.edu Received 11 May 2012; Accepted 14 July 2012 Academic Editor: Ilya M. Spitkovsky Copyright q 2012 Michael Dorff et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Given a collection of minimal graphs, M 1 ,M 2 ,...,M n , with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions on M 1 ,M 2 ,...,M n 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. 1. Introduction Consider a surface M in R 3 . Definition 1.1. The normal curvature at a point p ∈ M in the w direction is kw α ′′ · n, 1.1 where n is the unit normal at p, w is a tangent vector of M at p, and α is an arclength parametrization of the curve created by the intersection of M with the the plane containing w and n. Definition 1.2. A minimal surface is a surface M with mean curvature H  k 1  k 2 2  0, 1.2 at all points p ∈ M, where k 1 and k 2 are the maximum and minimum normal curvature values at p.