Equidistribution of dilated curves on nilmanifolds: EQUIDISTRIBUTION OF DILATED CURVES
Equidistribution of dilated curves on nilmanifolds: EQUIDISTRIBUTION OF DILATED CURVES
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尼尔流形上扩张曲线的等分布：EQUIDISTRIBUTION OF DILATED Curves
DOI：
10.1112/jlms.12156
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Sun, Wenbo
中科院分区：
文献类型：
--
作者：
Kra, Bryna;Shah, Nimish A.;Sun, Wenbo
推广环面上测度族的经典结果，对于定义在零流形上的测度族，我们研究了该测度族等分布的条件，即弱拓扑上的测度收敛于上的哈尔测度的条件。我们给出了由膨胀过程定义的测度族的一般条件，给出了当测度族膨胀时均衡分布的充分必要条件，并给出了在密度为零的某个集合之外的所有膨胀都成立的条件。进一步，我们证明了这两种类型的均匀分布是不同的。
Generalizing classic results for a family of measures in the torus, for a familyof measures defined on a nilmanifold, we study conditions under which the family equidistributes, meaning conditions under which the measuresconverge asin the weaktopology to the Haar measure on. We give general conditions on a family of measures defined by a dilation process, showing necessary and sufficient conditions for equidistribution as the family dilates, along with conditions such that this holds for all dilates outside some set of density zero. Furthermore, we show that these two types of equidistribution are different.