Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces

2021/01/28 by Gursky, Matthew J., McKeown, Stephen E., Tyrrell, Aaron J.
#53C18 (Secondary) #53C40 #81T35 (Primary) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2101.11755

Abstract

We define a renormalized volume for a region in an asymptotically hyperbolic Einstein manifold that is bounded by a Graham-Witten minimal surface and the conformal infinity. We prove a Gauss-Bonnet theorem for the renormalized volume, and compute its derivative under variations of the minimal hypersurface.

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