Volume renormalization for conformally compact asymptotically hyperbolic   manifolds in dimension four
  We derive a new renormalized volume formula for conformally compact asymptotically hyperbolic manifolds in dimension four. The formula generalizes the ones given by Anderson, Albin, and Chang-Qing-Yang for the case of Poincare-Einstein manifolds. We also derive variational formulas for the renormalized seen as a functional on the manifold. 
Shih-Tsai Feng
math.DG