On the dimension drop conjecture for diagonal flows on the space of lattices

Dmitry Kleinbock, Shahriar Mirzadeh

Let $X=G/\Gamma$, where $G$ is a Lie group and $\Gamma$ is a lattice in $G$, let $U$ be an open subset of $X$, and let $\{g_t\}$ be a one-parameter subgroup of $G$. Consider the set of poi…