Mathematical Sciences: Applications of Functional Analysis and Geometric Measure Theory

数学科学：泛函分析和几何测度理论的应用

• 批准号: 8701617
• 负责人: Frederick Almgren
• 金额: $ 18.83万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701617&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Applications; Functional; Analysis

Almgren will continue his long term program of research in the geometric calculus of variations and its applications. The objective is to seek a better understanding of the geometric structure of surfaces minimizing the integrals of parametric integrands. A specific example would be certain area minimizing surfaces. He will also study the evolution of surfaces towards such minimization and the feasibility of constructing algorithms with which to compute the mathematical framework for these analyses and their applications in continuum mechanics. A considerable effort will be devoted towards making many significant results more accessible. Geometric measure theory has proved extremely powerful in the hands of such practitioners as Almgren, but the techniques employed still remain unknown to the majority of researchers. Amongst the new directions to be followed will be investigations of relationships between area minimizing currents and various energies of mappings from the ambient space to spheres. Also work will be carried out into flows in spaces of rectifiable currents and varifolds.

Almgren将继续他的长期研究计划， 几何变分法及其应用的 目的是寻求更好地理解几何 最小化参数积分的曲面结构 被积函数一个具体的例子是某些面积最小化 表面。他还将研究表面的演变， 这种最小化和构建算法的可行性 用它来计算数学框架， 分析及其在连续介质力学中的应用。 将作出相当大的努力， 更容易获得重大成果。几何测度理论 在这些实践者手中证明是非常强大的， Almgren，但所采用的技术仍然是未知的， 大多数研究人员。在新航向乐团中 其次将调查区域之间的关系 最小化电流和各种能量的映射从 周围空间到球体。还将开展工作， 在整流电流和变压器的空间中流动。