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 - <p style="text-align: justify;">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.</p>