Mathematical Sciences: Research in Differential Geometry andTopology

8900285 米克斯 首席研究员将研究各种 微分几何和微分拓扑学中的问题。 研究的主要目标是开发一个更深层次的 理解全局拓扑和几何性质 在三维空间中的曲面，满足一些很好的几何或 变分原理 将特别强调： 1. 适当嵌入的全局几何和拓扑 极小曲面：存在定理，拓扑 障碍，全曲率定理，共形结构， 拓扑唯一性，实例指数的计算， 的最小图的唯一性， 非紧边界区域上的次线性增长 2. 中常平均曲率曲面的整体几何 3-空间和双曲三维空间. 相关计算 问题的主题。 4. 三维空间中的合痕曲面几何。

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.