Mathematical Sciences: Research in Differential Geometry andTopology

8900285名首席研究员将研究微分几何和微分拓扑学中的各种问题。这项研究的主要目的是加深对三维空间中满足某些几何或变分原理的曲面的整体拓扑和几何性质的理解。1.真嵌入极小曲面的整体几何和拓扑：存在定理、拓扑障碍、全曲率定理、共形结构、拓扑唯一性、例子指数的计算、等距扩张、具有非紧边界的区域上次线性增长极小图的唯一性。3.三维和双曲空间中常平均曲率曲面的整体几何。与学科中的问题相关的计算。4.三维空间中等距曲面的几何。

8900285 Meeks The principal investigator will study a variety of problems in differential geometry and differential topology. The main goal of the research is to develop a deeper understanding of global topological and geometrical properties of surfaces in 3-space that satisfy some nice geometrical or variational principle. Particular emphasis will be placed upon: 1. The global geometry and topology of properly embedded minimal surfaces: existence theorems, topological obstructions, total curvature theorems, conformal structure, topological uniqueness, computation of the index of examples, extension of isometries, uniqueness of minimal graphs of sublinear growth over domains with noncompact boundary. 2. Global geometry of constant mean curvature surfaces in 3-space and hyperbolic 3-space.3. Computation relevant to problems in the subject. 4. Geometry of isotopy surfaces in 3-space.