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These original research papers have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian manifolds, and the second is to establish various existence and regularity theorems as well as the explicit constructions of such maps.

This volume contains two reports on harmonic maps, published in 1978 and 1988 by James Eells and Luc Lemaire, which have become standard references for this subject. A brief supplement reports on some recent developments in the theory.

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications.

The material covered by the book displays a solid interplay involving geometry, analysis and topology: in...