The Surveys in Differential Geometry are supplements to the Journal of Differential Geometry, which are published by International Press. They include significant invited papers combining original research and overviews of the most current research in specific areas of interest to the growing Journal of Differential Geometry community. The survey volumes serve as continuing references, inspirations for new research, and introductions to the variety of topics of interest to differential geometers. These supplements are published annually since 1999.

The world-renowned Journal of Differential Geometry sponsors a triannual conference at Harvard University which brings together mathematicians from all over the world. The third conference celebrated the 30th anniversary of the journal, and the 70th birthday of its founding editor, C. C. Hsiung. This volume (Vol.3) of Surveys in Differential Geometry is based on the lectures given during the 3rd conference of Journal of Differential Geometry.