Mathematical Sciences: Special Submanifolds

[403851]詹森这个奖支持对微分几何问题的数学研究。重点研究了李球几何中的Dupin超曲面和可变形曲面。我们将努力确定复射影平面中是否存在具有恒定负高斯曲率的最小曲面。这些问题涉及非常有趣的特殊子流形；它们的解决涉及到在偏微分方程系统与几何结构相结合的研究中出现的技术组合。这项工作可以应用于数学物理和几何。微分几何是数学的一个分支，它把分析方法和几何动机结合起来。这些问题往往来自物理世界的问题，比如在相对论、湍流、动力系统和混沌的研究中会发现的问题。＊＊＊

9403851 Jensen This award supports mathematical research on problems in differential geometry. The work focuses on Dupin hypersurfaces and deformable surfaces in Lie Sphere geometry. Efforts will be made to determine whether or not there exist minimal surfaces with constant negative Gaussian curvature in the complex projective plane. The problems involve special submanifolds of great interest; their solutions involve a combination of techniques arising in the study of systems of partial differential equations combined with geometric structures. Applications of the work may be expected in mathematical physics as well as geometry. Differential geometry is a branch of mathematics which combines methods of analysis with geometric motivation. The problems often derive from those of the physical world such as would be found in studies of relativity, turbulence, dynamical systems and chaos. ***