Penelope Gehring
Mantoulidis and Schoen constructed smooth asymptotically flat manifolds of dimension 3 with prescribed horizon boundary, whose mass can be made arbitrarily close to the optimal value in the Riemannian Penrose inequality, while the geometry of a neighborhood of the horizon is far from being rotationally symmetric; Cabrera Pacheco and Miao obtained a higher dimensional analog to this construction.
Recently, this construction was transferred to the 3-dimensional case for asymptotically hyperbolic manifolds and asymptotically flat electrically charged manifolds by Cabrera Pacheco, Cederbaum and McCormick, and Alaee, Cabrera Pacheco and Cederbaum, respectively. In this talk, we will discuss n-dimensional asymptotically hyperbolic charged manifolds, and Peñuela Diaz and my work on transferring the Mantoulidis and Schoen construction to this case.
