Mathematical Sciences: Riemannian Geometry of Lagrangian Submanifolds

首席研究员将研究 辛几何中的拉格朗日子流形。 这将 包括分析辛 结构和黎曼结构的Kahler流形。 这项调查将包括，作为一个示范案例，研究 极小子流形及其平均曲率演化 辛几何作为一种几何学， 在这个框架中，力学中的难题可以被 制定和解决。 主要研究者将使用 这个理论和复Kahler流形之间的联系 特别是与极小子流形有关的。 此类表面 以肥皂片为模型， 近年来的数学研究。

The principal investigator will study various aspects of Lagrangian submanifolds in symplectic geometry. This will involve an analysis of the relationship between symplectic structures and the Riemannian structure of Kahler manifolds. This investigation will include, as a model case, the study of minimal submanifolds and their mean curvature evolutions. Symplectic geometry has a long history of success as a framework in which difficult questions in mechanics can be formulated and solved. The principal investigator will use connections between this theory and complex Kahler manifolds especially as related to minimal submanifolds. Such surfaces are modeled by soap films and have been the objects of intense mathematical research in recent years.