论文标题
Riemannian表面的Gromov-Hausdorff限制的新不变的曲率限制在下面
New invariants of Gromov-Hausdorff limits of Riemannian surfaces with curvature bounded below
论文作者
论文摘要
令$ \ {x_i \} $为一系列紧凑型$ n $ - 二维的Alexandrov空间（例如Riemannian歧管），其曲率均匀限制在下面，在Gromov-Hausdorff中会收敛到Gromov-Hausdorff Sense to compact compact Alexandrov Space $ x $ x $。在第一作者的较早论文中，描述了（没有证据）$ x $上的整数值函数的构造；此功能包含有关序列的其他几何信息，例如$ x_i $ s的内在卷的限制。在本文中，我们考虑了封闭的2张曲面的序列，（1）在这种情况下证明了这种功能的存在； （2）对构造可能产生的功能进行分类。
Let $\{X_i\}$ be a sequence of compact $n$-dimensional Alexandrov spaces (e.g. Riemannian manifolds) with curvature uniformly bounded below which converges in the Gromov-Hausdorff sense to a compact Alexandrov space $X$. In an earlier paper by the first author there was described (without a proof) a construction of an integer valued function on $X$; this function carries additional geometric information on the sequence such as the limit of intrinsic volumes of $X_i$'s. In this paper we consider sequences of closed 2-surfaces and (1) prove the existence of such a function in this situation; and (2) classify the functions which may arise from the construction.
