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Two-Dimensional Geometric Variational Problems

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This monograph treats variational problems for mappings from a surface equipped with a conformal structure into Euclidean space or a Riemannian manifold. Presents a general theory of such variational problems, proving existence and regularity theorems with particular conceptual emphasis on the geometric aspects of the theory and thorough investigation of the connections with complex analysis. Among the topics covered are: Plateau's problem, the regularity theory of solutions, a variational approach for obtaining various conformal representation theorems, a general existence theorem for harmonic mappings, and a new approach to Teichmuller theory via harmonic maps.

Author(s): Jürgen Jost
Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Edition: 1
Publisher: Wiley
Year: 1991

Language: English
Pages: 250
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