Mathematical Sciences: Research in Several Complex Variables

首席研究员将研究三个项目， 多个复杂变量的区域。 第一个问题涉及嵌入 高维球面中的严格伪凸CR流形。 在第二个项目中，他将推广关于 凸域上小林度量及相关概念， CR歧管。 第三个项目涉及函数的研究 满足齐次复Monge-Ampere方程， 沿光滑流形沿着的规定的奇异行为。 曲面和它们的高维类似物， 流形，可能存在于多维空间一直是一个主题 几十年来数学家们都很感兴趣。 某些 表面，像克莱因瓶，不能放在三个- 没有强迫自相交的三维空间。 但这 表面可以被放置到四维空间中，而不需要这样的 路口 首席研究员将深入研究 流形的相关问题是基于，而不是基于真实的 多维空间，但在复杂的空间。

The principal investigator will study three projects in the area of several complex variables. The first concerns imbedding strictly pseudoconvex CR manifolds in higher-dimensional spheres. In the second project he will generalize certain theorems about the Kobayashi metric and related notions from convex domains and CR manifolds. The third project involves the study of functions satisfying homogeneous complex Monge-Ampere equations which have a prescribed singular behavior along a smooth manifold. How surfaces and their higher-dimensional analogues, called manifolds, may lie in multi-dimensional space has been a subject of great interest to mathematicians for many decades. Certain surfaces, like the Klein bottle, cannot be placed in three- dimensional space without forcing self intersections. But this surface can be placed into four-dimensional space without such intersections. The principal investigator will study deep related questions for manifolds which are based, not on real multi-dimensional space, but on complex spaces.