Robert Greene and Shiu-Yuen Cheng will continue their work in the geometry and function theory of complex manifolds. The use of methods of metric geometry in complex analysis has a long history, much of the recent work involves the construction of invariant metrics. They will be joined by Gerard Walschap who will investigate certain interesting types of submanifolds of manifolds with nonnegative sectional curvature. Greene's research will concentrate on the following three areas: differential geometric several complex variables; Riemannian geometry of noncompact and compact manifolds; fixed points of smooth maps of manifolds. Cheng will investigate Liouville type theorems for harmonic functions and minimal hypersurfaces with finite total curvature. Walschap will consider the codimension two case of the so-called soul theorem. This involves the investigation of compact, totally convex and totally geodesic submanifolds.
