Comparison Between Conformal Invariants for Conformally Compact Einstein Metrics: Some Counter-Example from the Metrics Developed by Pedersen (Journal of Mathematical Study, 2023)
The study of asymptotically hyperbolic Einstein metric is a rich field in theoretical physics and geometry. Pedersen introduced a family of examples for the dimension 4, and we look in this paper into the sign of some of its conformal invariant,namely renormalized volume and Yamabe-type constant. This brings some insights inthe study of conformally compact Einstein manifold, as the comparison of invariantsis already common practice.
Keywords: Conformally compact Einstein manifolds; Berger sphere at infinity; Renormalized volume; Yamabe-Escobar constant.