Volume renormalization for complete Einstein--K\"ahler metrics
Differential Geometry
2011-11-10 v2
Abstract
For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete K\"ahler metric of Fefferman. We compute the conformal anomaly in complex dimension two and apply the result to derive a renormalized Chern--Gauss--Bonnet formula. Relations between renormalized volume and the CR -curvature are also investigated.
Cite
@article{arxiv.math/0404455,
title = {Volume renormalization for complete Einstein--K\"ahler metrics},
author = {Neil Seshadri},
journal= {arXiv preprint arXiv:math/0404455},
year = {2011}
}
Comments
Minor corrections to the statements and proofs of the main theorem and corollary. Included the example of the Bergman metric on the ball. To appear in Differential Geometry and Its Applications