Yau will continue his investigations of geometric questions which relate to problems in physics. His investigations of Kahler metrics on low dimensional manifolds are of importance in superstring theory. The latter is currently being studied in the context of the search for a complete unified field theory. The existence of complete Kahler-Einstein metrics on Kahler manifolds has recently been related to the positivity of the first Chern class. This result, together with its implications for algebraic geometry, will be further investigated. In particular, for non-compact manifolds, the construction of such metrics with either negative or zero scalar curvature will be studied. Yau will also attempt to find a clear understanding of complete Kahler-Einstein metrics with zero Ricci curvature. These are extensively studied by particle physicists who are interested in superstring theory.
