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Abstract: Minimal hypersurfaces in hyperbolic space share many common features with self-expanders in Euclidean space, which model the behaviors of mean curvature flow coming out of cones. In this talk, I will discuss how to adapt the theory of self-expanders developed by Bernstein--Wang to prove a min-max theory in hyperbolic space and to show certain topological properties for minimal hypersurfaces with low entropies.