TY - JOUR T1 - Comparison Between Conformal Invariants for Conformally Compact Einstein Metrics: Some Counter-Example from the Metrics Developed by Pedersen AU - Fraux , Paul JO - Journal of Mathematical Study VL - 4 SP - 357 EP - 365 PY - 2024 DA - 2024/01 SN - 56 DO - http://doi.org/10.4208/jms.v56n4.23.04 UR - https://global-sci.org/intro/article_detail/jms/22326.html KW - Conformally compact Einstein manifolds, Berger sphere at infinity, Renormalized volume, Yamabe-Escobar constant. AB -

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 in the study of conformally compact Einstein manifold, as the comparison of invariants is already common practice.