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光谱几何中的问题。格林教授将尝试寻找可用于对非紧自同构群的域进行分类的生物全纯不变量。彼得森教授将研究流形的拓扑和几何与拉普拉斯算子的谱之间的关系。该奖项支持的博士后，S. Zhu，将研究拓扑和里奇曲率之间的关系。该奖项将支持微分几何中试图将全局拓扑信息与局部分析信息联系起来的工作。局部信息一般以微分方程或方程组的不变量形式表示。然后使用这些信息对域进行分类或获得对所考虑的集合的全局“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.