Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces

Published 28 Jan 2021 in math.DG, math-ph, and math.MP | (2101.11755v2)

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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