L² curvature and volume renormalization of AHE metrics on 4-manifolds

2000/11/08 by Michael T. Anderson, Anderson, Michael T. · 2 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.math/0011051

15 pages, several corrections made. To appear in Math. Research Letters

arxiv created 2001/02/07 · arxiv updated 2009/11/30

Abstract

This paper relates the boundary term in the Chern-Gauss-Bonnet formula on 4-manifolds M with the renormalized volume V, as defined in the AdS/CFT correspondence, for asymptotically hyperbolic Einstein metrics on M. In addition, we compute and discuss the differential or variation dV of V, or equivalently the variation of the L² norm of the Weyl curvature, on the space of such Einstein metrics.

Cited by

• Poincaré-Einstein 4-manifolds with conformally Kähler geometry
• On the Poincaré-Einstein manifolds with cylindrical conformal infinity

Related

• A remark on renormalized volume and Euler characteristic for ACHE 4-manifolds
• A note on renormalized volume functionals
• Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces
• Volume renormalization for conformally compact asymptotically hyperbolic manifolds in dimension four
• The renormalized volume and uniformisation of conformal structures