Special subvarieties of non-arithmetic ball quotients and Hodge Theory

Gregorio Baldi, Emmanuel Ullmo

Let $\Gamma \subset \mathrm{PU}(1,n)$ be a lattice, and $S_{\Gamma }$ the associated ball quotient. We prove that, if $S_{\Gamma }$ contains infinitely many maximal totally geodesic subvarieties,…