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Renormalized Volume for Singular Yamabe Metrics

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Graham, Robin

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Renormalized Volume for Singular Yamabe Metrics
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21
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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I will begin by reviewing the renormalized volume for Poincaré-Einstein metrics. I will then discuss an analogous construction of renormalized volume for singular Yamabe (a.k.a. Loewner-Nirenberg) metrics. I will conclude by describing joint work with Matt Gursky concerning an unexpected invariance property of the renormalized volume for singular Yamabe metrics in dimension 4 related to the Chern-Gauss-Bonnet formula and related phenomena for solutions of a singular σ2 Yamabe problem.