Boundary Rigidity in a fixed conformal class for Asymptotically Hyperbolic Manifolds

Abstract

Given two conformal asymptotically hyperbolic metrics which are either both simple or both negatively curved, we show that if their (marked) renormalized boundary distances coincide for some choices of conformal representatives in their conformal infinities, then the two metrics are equal.

14 pages, 1 figure, comments are welcome