论文标题
缝合数据：从地球交叉口恢复歧管的几何形状
Stitching Data: Recovering a Manifold's Geometry from Geodesic Intersections
论文作者
论文摘要
令$（m，g）$为带边界的Riemannian歧管。我们表明，对每个大地测量的长度以及成对相交发生在相应的测量学上发生的知识允许恢复$（m，g）$的几何形状（假设$（M，G）$承认均匀半径的Riemannian项圈。我们将此知识称为“缝合数据”。然后，我们提出一个边界测量类型问题，称为“延迟碰撞数据问题”，并应用了我们对缝合数据的第一个结果，以从碰撞数据中恢复几何形状（对歧管有一些合理的几何限制）。
Let $(M,g)$ be a Riemannian manifold with boundary. We show that knowledge of the length of each geodesic, and where pairwise intersections occur along the corresponding geodesics allows for recovery of the geometry of $(M,g)$ (assuming $(M,g)$ admits a Riemannian collar of a uniform radius). We call this knowledge the 'stitching data'. We then pose a boundary measurement type problem called the 'delayed collision data problem' and apply our first result about the stitching data to recover the geometry from the collision data (with some reasonable geometric restrictions on the manifold).
