亚线性双 Lipschitz 等价与可解李群的准等距分类
Sublinear Bilipschitz Equivalence and the Quasiisometric Classification of Solvable Lie Groups
AI总结：
本文通过亚线性双 Lipschitz 等价理论区分可解李群的准等距类别，揭示了高维非单模可解群的不可数多个准等距类。
摘要：
我们证明了一个关于亚线性双 Lipschitz 等价的产品定理，该定理推广了 Kapovich、Kleiner 和 Leeb 在产品空间之间准等距关系的经典工作。我们利用该产品定理来区分某些可解群的准等距类别，这些群具有相同的维度、锥维度和德恩函数；实际上，我们通过亚线性双 Lipschitz 等价来区分它们，这比准等距更强。作为应用，我们恢复了 Bourdon 和 Rémy 用不同群最近得到的结果，即存在不可数多个不可分解、非单模、高维可解李群的准等距类别。
英文摘要：
We prove a product theorem for sublinear bilipschitz equivalences which generalizes the classical work of Kapovich, Kleiner and Leeb on quasiisometries between product spaces. We employ our product theorem to distinguish up to quasiisometry certain families of solvable groups which share the same dimension, cone-dimension and Dehn function; actually we do this by distinguishing them up to sublinear bilipschitz equivalence, which is slightly stronger. As an application, we recover the fact, recently obtained by Bourdon and Rémy with different groups, that there exists uncountably many quasiisometry classes of indecomposable, non-unimodular, high rank solvable Lie groups.
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