Pseudodifferential Operators and Geometric Analysis

这个项目的目的是提出复杂的方法分析弯曲的空间。我们的两个主要结果如下。首先，我们显著地改进了Berezin-Toeplitz算子作用于具有复相位的Fourier积分算子的象的已知事实。其次，我们研究了黎曼流形到几乎Kahler流形的Schrodinger映射流的初值问题。我们澄清了前面所有结果中关于目标空间的Kahler性质的假设的意义，并通过在与黎曼流形之间的映射相关的诱导丛上引入伪微分，成功地放弃了这个假设.

The purpose of this project is to present sophisticated methods of analysis on curved spaces. Two of our main results are the following. First, we significantly improved the known facts on Berezin-Toeplitz operators acting on the image of a certain Fourier integral operators with a complex phase. Secondly, we studied the initial value problem for the Schrodinger map flow of a Riemannian manifold to an almost Kahler manifold. We clarified the meaning of the assumption of the Kahler property of the target space in all the preceding results, and succeeded in dropping this assumption by introducing pseudodifferential calculus on induced bundle associated with a map between Riemannian manifolds.