Ultrarigid tangents of sub-Riemannian nilpotent groups

量化版本的潘苏渐近定理和米切尔坦格定理

Quantitative versions of Pansu Asymptotic Theorem and of Mitchell Tangent Theorem

本文量化研究了测地黎曼群向其度量极限收敛的速度，并改进了现有文献中的相关界。

Nilpotent groups and biLipschitz embeddings into $L^1$

We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an $L^1$ space, then it is abelian. We reach this conclusion by proving that every Carnot group that biLipschitz embeds into $L^1$ is abelian. Our proof follows the work of Cheeger and Kleiner, by considering the pull-back distance of a Lipschitz map into $L^1$ and representing it using a cut measure. We show that such cut measures, and the induced distances, can be blown up and the blown-up cut measure is supported on "generic" tangents of the original sets. By repeating such a blow-up procedure, one obtai…

Carnot rectifiability of sub-Riemannian manifolds with constant tangent

We show that if $M$ is a sub-Riemannian manifold and $N$ is a Carnot group such that the nilpotentization of $M$ at almost every point is isomorphic to $N$, then there are subsets of $N$ of positive measure that embed into $M$ by bilipschitz maps. Furthermore, $M$ is countably $N$--rectifiable, i.e., all of $M$ except for a null set can be covered by countably many such maps.

次Finsler几何中切空间的综述及其对$\mathsf{CD}$条件失效的应用

A review of the tangent space in sub-Finsler geometry and applications to the failure of the $\mathsf{CD}$ condition

本文综述了次Finsler流形在测度Gromov-Hausdorff意义下切空间的构造，并利用幂零近似与Lebesgue测度标量倍数的刻画，证明了配备有界测度的三维接触次Finsler流形不满足Lott-Sturm-Villani曲率维数条件。

度量 Lie 群：齐性视角下的 Carnot-Carathéodory 空间

Metric Lie Groups. Carnot-Carathéodory spaces from the homogeneous viewpoint

本书探讨 Lie 群上左不变距离定义的非光滑几何，重点阐述 Carnot 群等度量 Lie 群在幂零群渐近锥、对称空间抛物边界及流形极限等数学语境中的核心作用。