Mathematical Sciences: Asymptotic Behavior and the SingularSet of Minimal Surfaces and Harmonic Maps

主要研究人员将研究几何变分问题和解的奇异性。Simon教授将集中研究极小曲面和调和映射的奇异集的结构。他还将考虑关于奇点方法的不对称性，包括唯一的切锥问题。怀特教授将研究极小曲面、极小曲面上的分支点、极小变差中切锥和切映射的唯一性以及调和映射的桥定理。该奖项将支持在微分几何和全球分析的一般领域的研究。微分几何是研究空间几何和定义在该空间上的解析概念之间的关系的学科。全局分析是通过拼凑局部信息来研究空间的整体几何和拓扑性质的学科。这些领域的数学在其他科学中的应用包括复杂分子结构、液体-气体边界和宇宙的大尺度结构。

The principal investigators will study geometric variational problems and singularities of solutions. Professor Simon will concentrate his research on the structure of the singular set of minimal surfaces and harmonic maps. He will also consider asympotics on approach to singular points including the unique tangent cone problem. Professor White will investigate the bridge theorem for minimal surfaces, branch points in minimal surfaces, uniqueness of tangent cones and tangent maps in minimal varieties and harmonic maps. This award will support research in the general area of differential geometry and global analysis. Differential geometry is the study of the relationship between the geometry of a space and analytic concepts defined on the space. Global analysis is the study of the overall geometric and topological properties of a space by piecing together local information. Applications of these areas of mathematics in other sciences include the structure of complicated molecules, liquid-gas boundaries, and the large scale structure of the universe.