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Volume 56, Issue 4
Comparison Between Conformal Invariants for Conformally Compact Einstein Metrics: Some Counter-Example from the Metrics Developed by Pedersen

Paul Fraux

DOI: 10.4208/jms.v56n4.23.04

J. Math. Study, 56 (2023), pp. 357-365.

Published online: 2024-01

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  • Abstract

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.

  • Keywords

Conformally compact Einstein manifolds, Berger sphere at infinity, Renormalized volume, Yamabe-Escobar constant.

  • AMS Subject Headings

l53C25, 30F45,58C35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JMS-56-357, author = {Fraux , Paul}, title = {Comparison Between Conformal Invariants for Conformally Compact Einstein Metrics: Some Counter-Example from the Metrics Developed by Pedersen}, journal = {Journal of Mathematical Study}, year = {2024}, volume = {56}, number = {4}, pages = {357--365}, abstract = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v56n4.23.04}, url = {http://global-sci.org/intro/article_detail/jms/22326.html} }
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.

Fraux , Paul. (2024). Comparison Between Conformal Invariants for Conformally Compact Einstein Metrics: Some Counter-Example from the Metrics Developed by Pedersen. Journal of Mathematical Study. 56 (4). 357-365. doi:10.4208/jms.v56n4.23.04
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