Mathematical Sciences: Differential Geometry, Partial Differential Equations and Several Complex Variables

主要研究人员将研究复杂微分几何和谱几何中的问题。格林教授将尝试寻找双全纯不变量，它可以用来对具有非紧自同构群的区域进行分类。彼得森教授将研究流形的拓扑和几何与拉普拉斯算符的谱之间的关系。由该奖项资助的博士后助理朱世民将研究拓扑学与利玛奇曲率之间的关系。该奖项将支持微分几何方面的工作，该工作试图将全局拓扑信息与局部分析信息联系起来。局部信息通常以微分方程式或方程组的不变量的形式表示。然后使用该信息对域进行分类或获得对正在考虑的集合的全局“形状”的限制。

The principal investigators will study problems in complex differential geometry and spectral geometry. Professor Greene will attempt to find biholomorphic invariants which can be used to classify domains with noncompact automorphism group. Professor Petersen will study the relationship between the topology and geometry of a manifold and the spectrum of the Laplace operator. The post doctoral associate supported by this award, S. Zhu, will study the relationship between topology and Ricci curvature. This award will support work in differential geometry which tries to relate global topological information to local analytic information. The local information generally is presented in the form of an invariant of a differential equation or system of equations. The information is then used to classify the domain or to obtain restrictions on the global "shape" of the set under consideration.