Mathematical Sciences: Geodesics and Minimal Surfaces in Manifolds with Non-negative Curvature

数学科学：测地线和非负曲率流形中的极小曲面

• 批准号: 9102212
• 负责人: Jianguo Cao
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102212&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geodesics; Minimal; Surfaces

The principal investigator intends to continue his study of geodesics and minimal surfaces in manifolds of non-negative curvature with particular emphasis on manifolds of dimension four. Minimal surface theory will be used to investigate the relationships between the sectional curvature and topology of a manifold. A minimal surface is a surface which may be characterized as one which has minimal surface area for any bounding curve on the surface. It may also be characterized as one which minimizes the "surface tension" energy or which has mean curvature zero. In some sense, a minimal surface is a two dimensional analog of a geodesic, a curve of least length joining two points. The principal investigator will use the theory of minimal surfaces to study relationships between the global properties of a space and local properties such as curvature.

首席研究员打算继续研究 非负流形中的测地线与极小曲面 曲率，特别强调四维流形。 最小曲面理论将用于研究 的截面曲率和拓扑结构之间的关系， 歧管 最小曲面是可以被表征为 一个具有最小表面积的任何边界曲线上， 面它也可以被描述为一个最小化 “表面张力”能量或平均曲率为零。在一些 在某种意义上，最小曲面是测地线的二维模拟， 连接两点的最短的曲线。校长 研究者将使用极小曲面理论来研究 空间的整体性质和局部性质之间的关系 像曲率这样的性质。