Renormalized Volume

A Note on Renormalized Volume Functionals

The asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) metric defines invariants of the AHE metric and of a metric in the induced conformal class at infinity. These have been of recent interest, motivated in part by the AdS/CFT correspondence in physics. In this paper we derive some new properties of these invariants. Let (X, g+) be AHE with smooth conformal infin...

Extended Obstruction Tensors and Renormalized Volume Coefficients

In recent years there has been a great deal of progress on the so-called σk-Yamabe problem. In [CF], Alice Chang and Hao Fang have suggested that a variant of this problem might also be fruitful to study. The main goal of this paper is to investigate the algebraic structure under conformal transformation of the renormalized volume coefficients, the curvature quantites considered by Chang-Fang. ...

The Weil–Petersson metric and the renormalized volume of hyperbolic 3-manifolds

Positivity of the Renormalized Volume of Almost-fuchsian Hyperbolic 3-manifolds

We prove that the renormalized volume of almost-Fuchsian hyperbolic 3-manifolds is non-negative, with equality only for Fuchsian manifolds.

Renormalized Lattice Perturbation Theory

Apparent large failures of perturbation theory in lattice gauge theory at g* 5 1.0 result from the use of the bare coupling constant of the lattice regulator in the perturbative expansion. They can be cured by the use of a coupling constant defined by some physical process. Thissituation is thesame as that encountered in dimensionally regularized perturbation theory, where the use of a coupling...