International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 724268, 9 pages
http://dx.doi.org/10.1155/2012/724268
Research Article

Convex Combinations of Minimal Graphs

Michael Dorff,1 Ryan Viertel,1 and Magdalena Wołoszkiewicz2

1Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
2Department of Mathematics, Maria Curie-Sklodowska University, 20-031 Lublin, Poland

Received 11 May 2012; Accepted 14 July 2012

Academic Editor: Ilya M. Spitkovsky

Copyright © 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.

Abstract

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.