Harmonic Maps and Constant Mean Curvature Surfaces

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Bakhandeh, Jafar | 2013

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 45673 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Bahraini, Alireza
Abstract:
This set is an introduction to a method for studying Constant Mean Curvature Surfaces (CMC) and Minimal Surfaces with harmonic maps . In recent years , integrable systems approaches for the construction of CMC surfaces in R3 have been developed . One of them , using finite type solutions of the sinh-Gordon equation .Another approach to CMC surfaces was developed by J. Dorfmeister, F. Pedit, and H. Wu in 2006 . It is commonly called the DPW method. The Gauss map of a CMC surface is a harmonic map , and in the DPW method every such harmonic map can be obtained from some holomorphic potential in a loop algebra . This method gives a description of all immersed CMC surfaces in R3 . in this paper we studying old and new method and finally we show how the DPW method can be used to construct some basic examples of CMC surfaces
Keywords:
Minimal Surfaces ; Constant Mean Curvature ; Harmonic Map