Convex Combinations of Minimal Graphs. (15th August 2012)

• Record Type: Journal Article
• Authors: Dorff, Michael; Viertel, Ryan; Wołoszkiewicz, Magdalena
• Other Names: Spitkovsky Ilya M. Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2012(2012)
• Publication Date: 2012-08-15
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2012/724268
• Languages: English
• ISSNs: 0161-1712

Abstract

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.