Mathematical Sciences: Research in Differential Geometry and Topology

数学科学：微分几何和拓扑研究

• 批准号: 9505101
• 负责人: William Meeks
• 金额: $ 11.97万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505101&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Differential; Geometry

9505101 Meeks A variety of problems in differential geometry and topology of minimal and constant mean curvature surfaces are proposed. Total Gaussian curvature results as well as topological obstruction results will be sought for complete minimal surfaces of finite total curvature. For infinite total curvature minimal surfaces, topological uniqueness, growth estimates and the index theory will be examined. Global properties of constant mean curvature surfaces will be studied. Computer graphics and (period) computations for some of these surfaces will also be pursued. Minimal surfaces and constant mean curvature surfaces were first systematically investigated by the Belgian physicist Plateau in his famous soap film experiments. These surfaces model physical surfaces where either the surface area is minimized by surface tension or in the case of a stable interface between two materials. In recent years, periodic minimal surfaces are used to model condensed matter on a molecular scale.

提出了微分几何和最小和常平均曲率曲面拓扑中的各种问题。对于有限总曲率的完全极小曲面，将寻求全高斯曲率的结果以及拓扑阻塞的结果。对于无限总曲率最小曲面，拓扑唯一性，增长估计和指标理论将被检查。将研究常平均曲率曲面的全局性质。计算机图形和（周期）计算的一些这些表面也将进行。比利时物理学家高原在他著名的肥皂膜实验中首次系统地研究了最小曲面和常平均曲率曲面。这些表面模拟物理表面，其中表面积被表面张力最小化，或者在两种材料之间的稳定界面的情况下。近年来，周期性最小表面被用于在分子尺度上模拟凝聚态物质。