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Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems

Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems
Catalogue Information
Field name Details
Dewey Class 516
Title Constant Mean Curvature Surfaces, Harmonic Maps and Integrable Systems ([EBook] /) / by Frédéric Hélein.
Author Hélein, Frédéric
Other name(s) SpringerLink (Online service)
Publication Basel : : Birkhäuser Basel : : Imprint: Birkhäuser, , 2001.
Physical Details 122 p. : online resource.
Series Lectures in mathematics / ETH Zürich
ISBN 9783034883306
Contents note 1 Introduction: Surfaces with prescribed mean curvature -- 2 From minimal surfaces and CMC surfaces to harmonic maps -- 2.1 Minimal surfaces -- 2.2 Constant mean curvature surfaces -- 3 Variational point of view and Noether’s theorem -- 4 Working with the Hopf differential -- 4.1 Appendix -- 5 The Gauss-Codazzi condition -- 5.1 Appendix -- 6 Elementary twistor theory for harmonic maps -- 6.1 Appendix -- 7 Harmonic maps as an integrable system -- 7.1 Maps into spheres -- 7.2 Generalizations -- 7.3 A new setting: loop groups -- 7.4 Examples -- 8 Construction of finite type solutions -- 8.1 Preliminary: the Iwasawa decomposition (for). -- 8.2 Application to loop Lie algebras -- 8.3 The algorithm -- 8.4 Some further properties of finite type solutions -- 9 Constant mean curvature tori are of finite type -- 9.1 The result -- 9.2 Appendix -- 10 Wente tori -- 10.1 CMC surfaces with planar curvature lines -- 10.2 A system of commuting ordinary equations -- 10.3 Recovering a finite type solution -- 10.4 Spectral curves -- 11 Weierstrass type representations -- 11.1 Loop groups decompositions -- 11.2 Solutions in terms of holomorphic data -- 11.3 Meromorphic potentials -- 11.4 Generalizations.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-3-0348-8330-6
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