Minimal Surfaces and Singular Geometry

最小曲面和奇异几何

• 批准号: 0203434
• 负责人: Frank Morgan
• 金额: $ 6万
• 依托单位: Williams College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0203434&HistoricalAwards=false
• 关键词: Minimal; Surfaces; Singular; Geometry

ABSTRACT DMS - 0203434.Frank Morgan will study minimal structures in singular universes: withconical singularities or with Lipschitz metrics, for example. He will alsostudy mathematical models for soap bubbles clusters and immiscible fluids"with multiplicities," following work of Fleming and White. Methods includestandard and innovative applications of geometric measure theory,differentiable geometry, differential equations, and techniques from theproof of the Double Bubble Conjecture. He will supervise relatedundergraduate research, especially on variations on the double bubbleproblem in various ambients and settings.The guiding principle of nature seems to be energy minimization, from themicrostructure of materials to black holes in the universe. As one of thesimplest examples, soap bubble clusters seek to minimize surface area. Ifsuccessful, Morgan's study of such problems will enhance our understandingof fundamental physical principles, with implications for the structure ofmaterials and the universe.

弗兰克·摩根将研究奇异宇宙中的最小结构：例如，圆锥奇点或Lipschitz度量。他还将研究数学模型的肥皂泡集群和不混溶流体的“多重性”，以下工作的弗莱明和白色。方法包括标准和创新的应用几何测量理论，微分几何，微分方程，和技术从thevening的双泡猜想。他将指导相关的本科生研究，特别是在各种环境和设置下的双气泡问题的变化。自然界的指导原则似乎是能量最小化，从物质的微观结构到宇宙中的黑洞。作为一个最简单的例子，肥皂泡簇寻求最小化表面积。如果成功，摩根对这些问题的研究将增强我们对基本物理原理的理解，并对物质和宇宙的结构产生影响。