New invariants of Gromov–Hausdorff limits of Riemannian surfaces with curvature bounded below
New invariants of Gromov–Hausdorff limits of Riemannian surfaces with curvature bounded below
复制标题
曲率下界的黎曼曲面的 Gromov-Hausdorff 极限的新不变量
作者：
S. Alesker;M. Katz;Roman Prosanov
设$${xi}$${xi}是曲率一致有界的紧n维Alexandrov空间(如黎曼流形)的序列，它在Gromov-Hausdorff意义下收敛到紧Alexandrov空间X。论文(Alesker in Arnold Math J 4(1)：1-17,2018)概述了(无需证明)X上的整值函数的构造；该函数带有关于序列的附加几何信息，例如$$X_i$$X_i的内蕴体积的极限。在这篇文章中，我们考虑闭2-曲面序列和(1)在这种情况下证明了这种函数的存在性；以及(2)对这种构造可能产生的函数进行了分类。
Let $${X_i}$$ { 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 . The paper (Alesker in Arnold Math J 4(1):1–17, 2018) outlined (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 the $$X_i$$ X i . 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.
影响因子：
2.2
作者：
J.H.G. Fu;T. Wannerer
通讯作者：
T. Wannerer