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: Wiley 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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author Michael Dorff
Ryan Viertel
Magdalena Wołoszkiewicz
author_facet Michael Dorff
Ryan Viertel
Magdalena Wołoszkiewicz
author_sort Michael Dorff
collection DOAJ
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.
format Article
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institution OA Journals
issn 0161-1712
1687-0425
language English
publishDate 2012-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-dbbf77a99d1d42f7bb22b13bb19966bf2025-08-20T02:21:30ZengWileyInternational 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
spellingShingle Michael Dorff
Ryan Viertel
Magdalena Wołoszkiewicz
Convex Combinations of Minimal Graphs
International Journal of Mathematics and Mathematical Sciences
title 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_short Convex Combinations of Minimal Graphs
title_sort convex combinations of minimal graphs
url http://dx.doi.org/10.1155/2012/724268
work_keys_str_mv AT michaeldorff convexcombinationsofminimalgraphs
AT ryanviertel convexcombinationsofminimalgraphs
AT magdalenawołoszkiewicz convexcombinationsofminimalgraphs