Mathematical Sciences: Differential Geometry, Partial Differential Equations and Several Complex Variables

Robert Greene和shu - yuen Cheng将继续他们在复杂流形的几何和函数理论方面的工作。度量几何方法在复分析中的应用有着悠久的历史，最近的许多工作都涉及到不变度量的构造。Gerard Walschap将加入他们，他将研究非负截面曲率流形的子流形的某些有趣类型。格林的研究将集中在以下三个领域：微分几何的几个复变量；非紧流形和紧流形的黎曼几何流形光滑映射的不动点。Cheng将研究调和函数和具有有限总曲率的极小超曲面的Liouville型定理。Walschap将考虑所谓灵魂定理的余维二情况。这涉及紧、全凸和全测地线子流形的研究。

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.