# Asymptotically hyperbolic extensions of Riemannian manifolds

#### 17.01.2019, 16:15  –  Haus 9, Raum 0.14 Forschungsseminar Differentialgeometrie

Penelope Gehring (Tübingen)

Mantoulidis and Schoen constructed smooth asymptotically flat initial data sets of dimension 3 with prescribed horizon boundary, whose mass can be made arbitrary close to the optimal value in the Riemannian Penrose inequality, while the geometry of the horizon is far from being rotationally symmetric; Cabrera Pacheco and Miao obtained a higher dimensional analog to this construction. Recently, Cabrera Pacheco, Cederbaum and McCormick made a similar construction in the asymptotically hyperbolic case. In this talk we will discuss the Mantoulidis–Schoen construction and the corresponding adaptation to obtain a higher dimensional analog for the asymptotically hyperbolic case.

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