A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation
This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Euclidean 3-space. Spectral data for such solutions are defined (following ideas of Hitchin and Bobenko) and the space of spectral data is described by an asymptotic characterization. Using methods of asymptotic estimates, the inverse problem for the spectral data is solved along a line, i.e. the solution u is reconstructed on a line from the spectral data. Finally, a Jacobi variety and Abel map for…
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Produktdetails
- ISBN: 978-3-030-01275-5
- EAN: 9783030012755
- Produktnummer: 28545537
- Verlag: Springer-Verlag GmbH
- Sprache: Englisch
- Erscheinungsjahr: 2019
- Seitenangabe: 334 S.
- Masse: H23.5 cm x B15.5 cm x D1.8 cm 522 g
- Auflage: 2018
- Abbildungen: Book; Bibliographie
- Reihenbandnummer: 2229
- Gewicht: 522
Über den Autor
Sebastian Klein obtained his doctorate at the Universität zu Köln in 2005 in differential geometry. After a 2-year postdoc stay at University College Cork (UCC), he moved to Universität Mannheim in 2008. Here his research focus expanded into geometric analysis and integrable systems. He was a temporary lecturer at UCC in 2016-17, and is at the moment a Privatdozent in Mannheim.
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