标题： 凸共紧对角作用的刚性 显示英文标题

标题： Rigidity of convex co-compact diagonal actions

摘要： 克莱纳-李布和奎特表明，与秩1对称空间相比，高秩对称空间中的凸子集非常刚性。 受此启发，我们考虑适当CAT(0)空间乘积中的凸子集$X_1\times X_2$，并证明对于任何两个在$X_i$上的凸共紧作用$\rho_i(\Gamma)$，其中$i=1, 2$，如果通过$\rho=(\rho_1, \rho_2)$在$X_1\times X_2$上的对角作用$\Gamma$也是凸共紧的，则在适当条件下，$\rho_1(\Gamma)$和$\rho_2(\Gamma)$具有相同的标记长度谱。 显示英文摘要

摘要： Kleiner-Leeb and Quint showed that convex subsets in higher-rank symmetric spaces are very rigid compared to rank 1 symmetric spaces. Motivated by this, we consider convex subsets in products of proper CAT(0) spaces $X_1\times X_2$ and show that for any two convex co-compact actions $\rho_i(\Gamma)$ on $X_i$, where $i=1, 2$, if the diagonal action of $\Gamma$ on $X_1\times X_2$ via $\rho=(\rho_1, \rho_2)$ is also convex co-compact, then under a suitable condition, $\rho_1(\Gamma)$ and $\rho_2(\Gamma)$ have the same marked length spectrum.