度量商与奇异圆锥-平坦曲面的格罗莫夫-豪斯多夫收敛
Gromov-Hausdorff Convergence of Metric Quotients and Singular Conic-Flat Surfaces
摘要：
给定度量空间$X$的度量变量$S$和$S_n$，$n \in \mathbb{N}$，给出了定义它们的数据的充分条件，保证$S$是$S_n$的Gromov-Hausdorff极限.这些条件是公认的度量矩阵的平面多边形确定的侧配对称为普通纸折叠计划。特别是，给出了具体的例子序列的二维圆锥平坦的领域收敛到球是圆锥平坦的，除了周围的某些奇点，其中一些具有无界曲率的意义上的比较几何。
英文摘要：
Given metric quotients $S$ and $S_n$, $n \in \mathbb{N}$, of a metric space $X$, sufficient conditions are provided on the data defining them guaranteeing that $S$ is the Gromov-Hausdorff limit of $S_n$. These conditions are recognized within metric quotients of plane polygons determined by side-pairings known as plain paper-folding schemes. In particular, concrete examples are given of sequences of two-dimensional conic-flat spheres converging to spheres that are conic-flat except around certain singularities, some of them with unbounded curvature in the sense of comparative geometry.
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