Geometric Structures and Topology

研究曲面或其高维模拟流形的解析不变量与几何结构、曲率和拓扑之间的关系是光谱几何的主要问题之一。另一方面，有许多研究是逆问题，即与ct扫描仪和无损检测相关的数学问题。这里，我们考虑具有边界的流形上的谱逆问题，它位于上述两个场的交点上。特别是在只知道有误差的不完全解析数据的情况下，考虑了边界距离与内度规和拓扑的关系，从而确定了几何结构的稳定性。

It is one of the main problems to investigate relations between analytic invariants of surfaces or its higher dimensional analogue manifolds and geometric structures, curvatures and topology, which is called the spectral geometry. On the other hands, there are many researches as inverse problems, which is the mathematics related to CT-scanner and non destructive investigation. Here, we consider the spectral inverse problem on manifolds with boundary, which lies the intersection of the above fields. Especially, relating to the stability that is how much know about the geometric structure when one only knows incomplete analytic data with errors, we consider relations of the boundary distance with the inner metric and topology.