论文标题
gromov-hausdorff公制标准和奇异圆锥形表面的收敛性
Gromov-Hausdorff Convergence of Metric Quotients and Singular Conic-Flat Surfaces
论文作者
论文摘要
给定的度量标$ s $和$ s_n $，$ n \ in \ mathbb {n} $的公制空间$ x $的$ n \，在数据上提供了足够的条件，确保它们保证$ s $是$ s_n $的Gromov-Hausdorff限制。这些条件在平面多边形的度量标准中被识别，由称为普通纸张方案的侧面对。特别是，给出了具体的示例，以二维圆锥形球形球的序列融合到圆锥形的球体，除非某些奇异性，否则有些在比较几何学上具有无界曲率的序列。
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.
