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BIRS Workshop Lecture Videos

Renormalized Volume for Singular Yamabe Metrics Graham, Robin


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 $\sigma_2$ Yamabe problem.

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