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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |