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PERIODIC MINIMAL SURFACES IN SEMIDIRECT PRODUCTS
Published online by Cambridge University Press: 15 October 2013
Abstract
In this paper we prove the existence of complete minimal surfaces in some metric semidirect products. These surfaces are similar to the doubly and singly periodic Scherk minimal surfaces in ${ \mathbb{R} }^{3} $. In particular, we obtain these surfaces in the Heisenberg space with its canonical metric, and in ${\mathrm{Sol} }_{3} $ with a one-parameter family of nonisometric metrics.
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- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 96 , Issue 1 , February 2014 , pp. 127 - 144
- Copyright
- Copyright ©2013 Australian Mathematical Publishing Association Inc.
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