Convergence of measures on compactifications of locally symmetric spaces
Convergence of measures on compactifications of locally symmetric spaces
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DOI：
10.1007/s00209-020-02558-w
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发表时间：
2018-09
影响因子：
0.8
通讯作者：
Christopher Daw;A. Gorodnik;E. Ullmo
中科院分区：
文献类型：
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作者：
Christopher Daw;A. Gorodnik;E. Ullmo
我们猜想算术局部对称空间的极大Satake紧化上的齐次概率测度集是紧的。更确切地说，给定S上的齐次概率测度序列，我们期望任何弱极限都是齐次的，并且支撑恰好包含在其中一个边界分量（包括S本身）中。我们介绍了几种工具来研究这个猜想，我们证明了它在一些情况下，包括whenand。
We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric spaceis compact. More precisely, given a sequence of homogeneous probability measures onS, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (includingSitself). We introduce several tools to study this conjecture and we prove it in a number of cases, including whenand.