Filling invariants of stratified nilpotent Lie groups
Filling invariants of stratified nilpotent Lie groups
复制标题
分层幂零李群的填充不变量
DOI：
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发表时间：
2015
影响因子：
0.8
通讯作者：
Moritz Gruber
中科院分区：
文献类型：
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作者：
Moritz Gruber
填充不变量是度量空间的度量，描述了等周不等式的行为。在这篇文章中，我们研究填充函数和高散度函数。我们证明了一类分层幂零李群的填充函数在低维增长一样快的欧氏空间和在高维慢于欧氏空间的填充函数。我们这样做，通过开发一个纯代数条件的李代数分层幂零李群。此外，我们找到了一个充分的标准，这样的群体有一个填充功能，在一个特殊的尺寸与增长更快的适当填充功能的欧几里德空间。进一步，我们给出了层幂零李群的高发散函数的界。
Filling invariants are measurements of a metric space describing the behaviour of isoperimetric inequalities. In this article we examine filling functions and higher divergence functions. We prove for a class of stratified nilpotent Lie groups that in the low dimensions the filling functions grow as fast as the ones of the Euclidean space and in the high dimensions slower than the filling functions of the Euclidean space. We do this by developing a purely algebraic condition on the Lie algebra of a stratified nilpotent Lie group. Further, we find a sufficient criterion for such groups to have a filling function in a special dimension with faster growth as the appropriate filling function of the Euclidean space. Further we bound the higher divergence functions of stratified nilpotent Lie groups.