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- W135879145 abstract "The aim of this paper is to give a new link between integrable systems and minimal surface theory. The dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps. Since a minimal surface in 3-space is a Willmore surface, its conformal Gauss map is harmonic and a dressing on the conformal Gauss map can be defined. We study the induced transformation on minimal surfaces in the simplest case, the simple factor dressing, and show that the well-known Lopez-Ros deformation of minimal surfaces is a special case of this transformation. We express the simple factor dressing and the Lopez-Ros deformation explicitly in terms of the minimal surface and its conjugate surface. In particular, we can control periods and end behaviour of the simple factor dressing. This allows to construct new examples of doubly-periodic minimal surfaces arising as simple factor dressings of Scherk's first surface." @default.
- W135879145 created "2016-06-24" @default.
- W135879145 creator A5003575412 @default.
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- W135879145 date "2014-09-18" @default.
- W135879145 modified "2023-10-16" @default.
- W135879145 title "Simple factor dressing and the Lopez-Ros deformation of minimal surfaces in Euclidean 3-space" @default.
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- W135879145 doi "https://doi.org/10.48550/arxiv.1409.5286" @default.
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