Rough $I$-convergence in cone metric spaces

Rough convergence of sequences in a cone metric space

Here we have introduced the idea of rough convergence of sequences in a cone metric space. Also it has been investigated how far several basic properties of rough convergence as valid in a normed linear space are affected in a cone metric space.

度量空间之间的拟对称与它们无限双曲锥之间的粗糙拟等距

Quasi-symmetries between metric spaces and rough quasi-isometries between their infinite hyperbolic cones

本文研究度量空间拟对称与无限双曲锥粗糙拟等距之间的对应关系，证明了三类推广结果：幂拟对称诱导粗糙拟等距、完备度量空间可实现为无限双曲锥的相对 Gromov 边界、可视 Gromov 双曲空间与其边界的无限双曲锥粗糙相似，从而将文献 [3] 中相关定理推广到无界空间和无限锥情形。

On the Assouad dimension and convergence of metric spaces

We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric space is bounded from below by that of any pseudo-cone of it. We exhibit a example containing all compact metric spaces as pseudo-cones, and examples containing all proper length spaces as tangent cones or asymptotic cones.

洛伦兹空间的收敛性与广义锥的曲率界

Convergence of Lorentzian spaces and curvature bounds for generalized cones

本文引入了洛伦兹前长度空间的收敛概念，证明了时状曲率和时状曲率-维度界在该收敛下稳定，并展示了广义洛伦兹锥在该收敛下的适应性，最终获得预紧致定理。

随机锥与多面体弱收敛的一种新方法

A new approach to weak convergence of random cones and polytopes

提出一种证明随机多面体弱收敛的新方法，并应用于随机锥形剖分，证明其重标度Schläfli随机锥轮廓弱收敛于Poisson超平面剖分的典型胞腔。

On the rate of convergence to the asymptotic cone for nilpotent groups and subFinsler geometry

Addressing a question of Gromov, we give a rate in Pansu's theorem about the convergence in Gromov-Hausdorff metric of a finitely generated nilpotent group equipped with a left-invariant word metric scaled by a factor 1/n towards its asymptotic cone. We show that due to the possible presence of abnormal geodesics in the asymptotic cone, this rate cannot be better than n^{1/2} for general non-abelian nilpotent groups. As a corollary we also get an error term of the form vol(B(n))=cn^d + O(n^{d-2/(3r)}) for the volume of Cayley balls of a nilpotent group with nilpotency class r. We also state a …