Key to H. C. Wang's quantitative study of Zassenhaus neighbourhoods of non-compact semisimple Lie groups are two constants that depend on the root system of the corresponding Lie algebra. This article extends the list of values for Wang's constants to the exceptional Lie groups and also removes their dependence on dimension. The first application is an improved upper sectional curvature bound for a canonical left-invariant metric on a semisimple Lie group. The second application is an explicit uniform positive lower bound for arbitrary orbifold quotients of a given irreducible symmetric space of non-compact type.

中文翻译：

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关于对称空间的单商的体积

Wang HC对非紧实半简单Lie群的Zassenhaus邻域进行定量研究的关键是两个常数，它们取决于相应Lie代数的根系统。本文将Wang常数的值列表扩展到特殊的Lie组，并消除了它们对维的依赖。第一个应用是针对半简单李群上的规范左不变度量的改进的上部截面曲率。第二个应用是给定不可约非对称类型对称空间的任意二元商的显式一致正下界。