Singularity Behavior in Some Geometric Variational Problems

一些几何变分问题中的奇异性行为

• 批准号: 9704367
• 负责人: Robert Hardt
• 金额: $ 15.9万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704367&HistoricalAwards=false
• 关键词: Singularity; Behavior; Some; Geometric; Variational

9704367 Hardt This project lies in the general area of geometric variational calculus, dealing with the behavior of singularities and various energy critical objects. Some specific investigations focus on n-harmonic maps and biharmonic maps, regularity theory for minimal surfaces with boundary, and isoperimetric and sobolev inequalities in varieties. Geoemtric variational calculus involves questions about various extremal and/or optimal objects amongst families of objects satisfying a common set of constraints. Area and energy minimizing surfaces are among the objects studied in this theory. These surfaces have applications in materials science as they can be used to model condensed matter.

小行星9704367 这个项目在于几何变分学的一般领域，处理奇异性和各种能量临界对象的行为。一些具体的研究集中在n-调和映射和双调和映射，带边界极小曲面的正则性理论，等周不等式和Sobolev不等式的品种。 几何变分涉及的问题，各种极值和/或最佳对象之间的家庭的对象满足一组共同的约束。面积和能量最小化的表面是在这个理论中研究的对象。这些表面在材料科学中有应用，因为它们可以用来模拟凝聚态物质。