Relative entropy of hypersurfaces in hyperbolic space (Q6112908)

The author considers a special family of hypersurfaces in the hyperbolic space \({\mathbb H}^{n+1}\), which are asymptotic in a certain sense. For two such hypersurfaces, a relative entropy is defined and is expressed in terms of a renormalized area. For a mean curvature flow of these hypersurfaces, located in a thin neighborhood of a fixed minimal hypersurface \(\Sigma\) in \({\mathbb H}^{n+1}\), a monotonicity formula for the relative entropy is proven. These properties follow from some more general results, involving weighted relative entropies.