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Volume renormalization for complete Einstein--Kähler metrics

Neil Seshadri
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Abstract

For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete Kähler 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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Neil Seshadri. 2006-05-26. Volume renormalization for complete Einstein--Kähler metrics. https://doi.org/10.1016/j.difgeo.2007.02.004

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