Convex Combinations of Minimal Graphs

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 combinati...

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Main Authors:	Michael Dorff, Ryan Viertel, Magdalena Wołoszkiewicz
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/2012/724268

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spelling	doaj-dbbf77a99d1d42f7bb22b13bb19966bf2020-11-25T00:52:31ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/724268724268Convex Combinations of Minimal GraphsMichael Dorff0Ryan Viertel1Magdalena Wołoszkiewicz2Department of Mathematics, Brigham Young University, Provo, UT 84602, USADepartment of Mathematics, Brigham Young University, Provo, UT 84602, USADepartment of Mathematics, Maria Curie-Sklodowska University, 20-031 Lublin, PolandGiven 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.http://dx.doi.org/10.1155/2012/724268
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Michael Dorff Ryan Viertel Magdalena Wołoszkiewicz
spellingShingle	Michael Dorff Ryan Viertel Magdalena Wołoszkiewicz Convex Combinations of Minimal Graphs International Journal of Mathematics and Mathematical Sciences
author_facet	Michael Dorff Ryan Viertel Magdalena Wołoszkiewicz
author_sort	Michael Dorff
title	Convex Combinations of Minimal Graphs
title_short	Convex Combinations of Minimal Graphs
title_full	Convex Combinations of Minimal Graphs
title_fullStr	Convex Combinations of Minimal Graphs
title_full_unstemmed	Convex Combinations of Minimal Graphs
title_sort	convex combinations of minimal graphs
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2012-01-01
description	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.
url	http://dx.doi.org/10.1155/2012/724268
work_keys_str_mv	AT michaeldorff convexcombinationsofminimalgraphs AT ryanviertel convexcombinationsofminimalgraphs AT magdalenawołoszkiewicz convexcombinationsofminimalgraphs
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Convex Combinations of Minimal Graphs

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