Mathematical Sciences: RUI: Minimal Surfaces, Clusters, and Singular Geometry

数学科学：RUI：最小曲面、簇和奇异几何

• 批准号: 9625641
• 负责人: Frank Morgan
• 金额: $ 9.6万
• 依托单位: Williams College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-15 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9625641&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Minimal; Surfaces

9625641 Morgan This proposal lies in the area of minimal surfaces and more generally constant mean curvature surfaces. The investigator plans to use methods from geometric measure theory and calibrations along with computer simulation. More specifically, the proposed topics include: least perimeter partitions of space into equal volumes; minimizing properties of equilibrium configurations. There is also an undergraduate research project involving double bubbles and minimal clusters - this is done under the Research at Undergraduate Institutions Program. The so called Double Bubble Conjecture on the least-area way to enclose and separate two regions of equal volume was recently given a computer proof, and this is to be further pursued in this project. Minimal surfaces and minimizing clusters arise as physical surfaces in a variety of setting as they have certain extremal properties, e.g., surface area minimizing and energy minimizing. Smap film and soap bubble surfaces provide readily available examples of minimal surfaces and constant mean curvature surfaces. Also, minimal clusters and periodic minimal surfaces can be used to model compound polymer systems and condensed matter in general.

小行星9625641 这个建议在于最小曲面和更一般的常平均曲率曲面的区域。研究人员计划使用几何测量理论和校准方法，沿着计算机模拟。更具体地说，建议的主题包括：最小周长的空间分割成相等的体积，最小化的平衡配置的属性。还有一个涉及双气泡和最小集群的本科研究项目-这是在本科院校研究计划下完成的。关于以最小面积法将两个等体积的区域包围并分隔开的所谓双泡猜想，最近得到了计算机证明，这将在本项目中进一步研究。 最小曲面和最小化簇作为物理曲面出现在各种设置中，因为它们具有某些极值属性，例如，表面积最小化和能量最小化。Smap薄膜和肥皂泡曲面提供了最小曲面和常平均曲率曲面的现成示例。此外，最小团簇和周期性最小表面可以用来模拟化合物聚合物系统和凝聚态物质一般。