紧半单李群中的测度增长与 Kemperman 逆问题
群论
2023-03-29 v1 组合数学
摘要
设 为紧半单李群， 为 上的归一化 Haar 测度， 为可测集。我们证明 其中绝对常数 （独立于 的选取）被定量确定。我们还给出了无环商连通紧群的一个更一般结果，并解决了 1964 年的 Kemperman 逆问题。
引用
@article{arxiv.2303.15628,
title = {Measure growth in compact semisimple Lie groups and the Kemperman Inverse Problem},
author = {Yifan Jing and Chieu-Minh Tran},
journal= {arXiv preprint arXiv:2303.15628},
year = {2023}
}
备注
50 pages; the paper subsumes the compact case of arxiv:2006.01824. The proof now is simplified and effective, the smallness assumption in the main theorem is removed, and the model theoretical arguments are no longer needed. For the non-compact case, a more straightforward proof using the non-abelian Brunn-Minkowski inequality was obtained by An, Zhang, and the authors in arXiv:2111.05236