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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.

Paul Fraux. (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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