Mathematical Sciences: Geometry and Topology of Riemannian Manifolds

两位研究者将继续研究微分几何及相关领域的全球性问题。一个将研究一类曲率从下有界，直径从上有界的黎曼流形的Gromov-Hausdorff闭包。在这种情况下，结构问题、有限性问题和唯一性问题将根据体积和新的度量不变量（如过量和三角）进行研究。第二个博士后研究员将研究某些类型流形的几何和拓扑之间的关系。有限度、黎曼振动、注入半径和刚度将是这些空间的研究方向。几何学家多年来一直致力于理解广义曲面的曲率与其形状之间的关系。这些研究者已经证明，曲率在下面有界，直径在上面有界的曲面，一定有特定的形状。在这个项目中，他们将扩展这项研究，包括具有其他理想特性的表面。

Two investigators will continue their studies of global problems in differential geometry and related areas. One will investigate the Gromov-Hausdorff closure of the class of Riemannian manifolds with curvature bounded from below and diameter from above. In this setting, structure problems, finiteness problems, and uniqueness problems will be investigated in terms of volume and new metric invariants such as excess and triameter. The second postdoctoral investigator will study the relationship between geometry and topology of certain classes of manifolds. Finiteness, Riemannian fibrations, injectivity radius, and rigidity will be among the aspects of these spaces to be investigated. For many years geometers have worked to understand the relationship between the curvature of generalized surfaces and their shape. These investigators have proven that such surfaces which have curvature bounded below and diameter bounded above, must have certain specified shapes. In this project they will expand this investigation to include surfaces with other desireable properties.