李群的渐近锥面与锥等价
Asymptotic cones of Lie groups and cone equivalences
摘要：
引入了度量空间之间的锥Bilipschitz等价。这些映射比拟等距映射更一般，它们在渐近锥面之间诱导出一个bilipschitz同胚。非平凡的例子出现在李群的上下文中，因此，我们证明了研究的渐近锥面的连通李群可以减少到可解李群的一种特殊形式。我们还研究了幂零群的渐近锥面。
英文摘要：
We introduce cone bilipschitz equivalences between metric spaces. These are maps, more general than quasi-isometries, that induce a bilipschitz homeomorphism between asymptotic cones. Non-trivial examples appear in the context of Lie groups, and we thus prove that the study of asymptotic cones of connected Lie groups can be reduced to that of solvable Lie groups of a special form. We also focus on asymptotic cones of nilpotent groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
