论文标题
凸相结合作用在投影空间中的动力学特性
Dynamical properties of convex cocompact actions in projective space
论文作者
论文摘要
我们在舞Danciger-gueritaud-kassel的意义上对凸的共同组合的动作进行了动态表征：我们表明，$ \ Mathbb {r} \ mathrm {p}^d $在$ \ mathbb {r}^d $上等同于该组的扩张属性等于千边形的属性，偶尔在限制范围内，在限制范围内相同。作为一种应用，我们为相对于凸共聚子组集合的组提供了足够且必要的条件。我们表明，在这种情况下的凸共聚性等同于从Bowditch边界到该组的极限集的商的同态同态存在，而其外围亚组的极限集。
We give a dynamical characterization of convex cocompact group actions on properly convex domains in projective space in the sense of Danciger-Gueritaud-Kassel: we show that convex cocompactness in $\mathbb{R} \mathrm{P}^d$ is equivalent to an expansion property of the group about its limit set, occuring in different Grassmannians. As an application, we give a sufficient and necessary condition for convex cocompactness for groups which are hyperbolic relative to a collection of convex cocompact subgroups. We show that convex cocompactness in this situation is equivalent to the existence of an equivariant homeomorphism from the Bowditch boundary to the quotient of the limit set of the group by the limit sets of its peripheral subgroups.
