A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation

- Part I Spectral Data. - Introduction. - Minimal Immersions into the 3-Sphere and the Sinh-Gordon Equation. - Spectral Data for Simply Periodic Solutions of the Sinh-Gordon Equation. - Part II The Asymptotic Behavior of the Spectral Data. - The Vacuum Solution. - The Basic Asymptotic of the Monodromy. - Basic Behavior of the Spectral Data. - The Fourier Asymptotic of the Monodromy. - The Consequences of the Fourier Asymptotic for the Spectral Data. - Part III The Inverse Problem for the Monodromy. - Asymptotic Spaces of Holomorphic Functions. - Interpolating Holomorphic Functions. - Final Description of the Asymptotic of the Monodromy. - Non-special Divisors and the Inverse Problem for the Monodromy. - Part IV The Inverse Problem for Periodic Potentials (Cauchy Data). - Divisors of Finite Type. - Darboux Coordinates for the Space of Potentials. - The Inverse Problem for Cauchy Data Along the Real Line. - Part V The Jacobi Variety of the Spectral Curve. - Estimate of Certain Integrals. - Asymptotic Behavior of 1-Forms on the Spectral Curve. - Construction of the Jacobi Variety for the Spectral Curve. - The Jacobi Variety and Translations of the Potential. - Asymptotics of Spectral Data for Potentials on a Horizontal Strip. - Perspectives.

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.