Volume renormalization for complete Einstein--Kähler metrics

Details Volume renormalization for complete Einstein--Kähler metrics Volume renormalization for complete Einstein--Kähler metrics

2004-04-26

arxiv.org/abs/math/0404455v2

Diff. Geom. Appl. 25 (2007) 356--379

Mathematics

Differential Geometry

Minor corrections to the statements and proofs of the main theorem and corollary. Included the example of the Bergman metric o

Scientific paper

10.1016/j.difgeo.2007.02.004

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 $Q$-curvature are also investigated.

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