Mathematical Sciences: Geometric Invariants, Pseudodifferential Operators and Several Complex Variables

主要的研究人员将研究严格伪凸流形上的全局不变量，这些不变量是作为完全Kaehler度量的重整化陈类出现的。他将继续他的伪微分算子演算的研究，以适应类似于Bergman-Laplace算子的退化算子的研究。我们的目标是获得将重整化的陈数与退化椭圆复数的“解析”指数联系起来的指数公式。他还将继续研究嵌入三维CR流形的问题。多年来，数学家们一直在研究某些微分算子在延展到无穷远的超曲面上的行为。这项研究起源于牛顿微积分。在这个项目中，主要的研究人员将分析在非常大的“接近”无穷大的区域上有很大变化的运算符。过去，只在局部变化较小的算子方面取得了进展。

The principal investigator will study global invariants on strictly pseudoconvex manifolds that arise as renormalized Chern classes for complete Kaehler metrics. He will continue his study of pseudodifferential operator calculi adapted to the study of degenerate operators similiar to the Bergman-Laplace operator. A goal will be to obtain index formulae relating the renormalized Chern numbers to "analytic" indices for degenerate elliptic complexes. And he will continue an investigation of the problem of embedding three dimensional CR-manifolds. For many years mathematicians have studied the behavior of certain differential operators on hypersurfaces which extend off to infinity. This study has its origins in the calculus of Newton. In this project the principal investigator will analyze operators which have large variations over very large domains "near" infinity. In the past, only progress on operators which have small local variations was made.