Continuity of Limit Cones in the Space of Anosov Representations

For discrete subgroups of semisimple Lie groups, the limit cone serves as a key invariant in studying asymptotic properties. Anosov subgroups, well-known for their rich geometric and dynamical features, form an important class of these discrete subgroups. A natural question arises: does the limit cone vary continuously along deformations of Anosov subgroups? In this talk, we discuss a sufficient condition for such continuity, along with applications like the continuity of the growth indicators along deformations. Based on joint work with Hee Oh.