The uniform topology of rough Riemannian metrics

粗糙黎曼结构近年来被认为是解析对象的一类重要的几何不变性。虽然一些直接的事实是已知的，但还没有对这一组进行系统的研究。这里的目标是通过赋予它一个扩展的距离度量来研究这个集合。这包括理解这个空间中序列的极限，并将这个空间与其他已知的拓扑（如measuredgromov - hausdorff拓扑）联系起来。

Rough Riemannian structures have been identified in recent times as an important class of geometric invariances of analytic objects. Though some immediate facts are known, there has not been a systematic study of this set. The goal here would be to study this set by endowing it with an extended distance metric. This includes understanding limits of sequences in this space and relating this space to other well-known topologies, such as the measured-Gromov-Hausdorff topology.