Mathematical Sciences: Differential Geometry and Partial Differential Equations

首席研究员将继续研究 几何变分问题他将研究稳定性， 任意空间极小曲面的全纯性质 余维，发展了拉格朗日极小的存在性理论 卡勒-爱因斯坦流形的子流形。他还将研究 非正奇异空间调和映射的结构 曲率和确定一般条件下， Bochner方法可以用来建立刚性定理。 该奖项将支持一般领域的研究， 微分几何和全局分析。微分几何 是研究空间的几何形状 和空间上定义的分析概念。全球分析是 对物体的整体几何和拓扑性质的研究 一个空间，通过拼凑当地的信息。的应用 这些数学领域的其他科学包括 复杂的分子结构，液-气边界， 宇宙的大尺度结构

The principal investigator will continue his research on geometric variation problems. He will study stability and holomorphicity properties of minimal surfaces in arbitrary codimension, and develop existence theory for Lagrangian minimal submanifolds of Kahler-Einstein manifolds. He will also study the structure of harmonic maps into singular spaces of nonpositive curvature and determine general conditions under which the Bochner method can be used to establish rigidity theorems. 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.