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: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/724268 |
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| _version_ | 1850166263098114048 |
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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 |
| id | doaj-art-dbbf77a99d1d42f7bb22b13bb19966bf |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |