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

罗伯特格林和郑兆元将继续他们的工作 复流形的几何和函数理论使用 复分析中度量几何的方法有着悠久的历史， 历史上，最近的大部分工作都涉及建造 不变度量杰拉德·沃尔沙普将加入他们的行列， 将研究某些有趣类型的子流形， 具有非负截面曲率的流形。 格林的研究将集中在以下三个方面 领域：微分几何多复变; 非紧和紧流形的黎曼几何;不动 流形光滑映射的点程会调查 调和函数的Liouville型定理与极小 具有有限全曲率的超曲面沃尔沙普会考虑 所谓灵魂定理的余维二的情况。这 涉及研究紧的，全凸的和全 测地子流形

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.