Two-Dimensional Geometric Variational Problems

by Jürgen Jost

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 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.

250 pages, Paperback

First published March 29, 1991

About the author

Jürgen Jost is a German mathematician. He has been a director of the Max Planck Institute for Mathematics in the Sciences in Leipzig since 1996.