The model space of an asymptotically hyperbolic (AH) manifold is hyperbolic space, realized as the Poincaré ball. More generally, AH manifolds arise as the interiors of compact manifolds with boundary, equipped with complete metrics admitting a suitable conformal compactification. I will discuss a new invariant for a large class of submanifolds in certain AH manifolds. This invariant emerges in the derivation of Dirichlet eigenvalue lower bounds for such submanifolds, and can be used to rule out the existence of compact minimal submanifolds in specific asymptotically hyperbolic settings. This is joint work with Jeffrey Case, Aaron Tyrrell, and Dawit Yishak.
