Lectures on Harmonic Maps (Conference Proceedings and Lecture Notes in Geometry & Topology, Vol. 2)

A presentation of research on harmonic maps, based on lectures given at the University of California, San Diego. Schoen has worked to use the Fells/Sampson theorem to reprove the rigidity theorem of Masfow and superrigidity theorem of Marqulis. Many of these developments are recorded here. From the beginning harmonic maps were studied in connection with the theory of minimal surfaces. In 1985, the authors presented a series of lectures at the University of California at San Diego on the subject of harmonic maps. Most of these lectures are collected here as Part I. Part I of the book is devoted to harmonic maps defined on Riemann surfaces. Part II was added much more recently, and comprises part of the thesis of the first author, the work of N. Korevaar and the second author, and applications to geometry by the authors. The final chapter is due to J. Jost and the second author. This book presents some of the latest research on this topic from two of the foremost researchers in the field. This volume presents important results from two well-known researchers in this field. The book can serve as an important reference tool for students working in this area. Included is a chapter on "Harmonic Maps and Superrigidity" written by J. Jost and S.-T. Yau.