Two-Dimensional Geometric Variational Problems

Two-Dimensional Geometric Variational Problems

by Jurgen Jost


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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.

Product Details

ISBN-13: 9780471928393
Publisher: Wiley
Publication date: 03/29/1991
Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts Series , #12
Pages: 250
Product dimensions: 6.14(w) x 9.53(h) x 0.87(d)

Table of Contents

Examples, Definitions, and Elementary Results.

Regularity and Uniqueness Results.

Conformal Representation.

Existence Results.

Harmonic Maps Between Surfaces.

Harmonic Maps and Teichmüller Spaces.




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