Renormalized Chern-Gauss-Bonnet formula for complete Kahler-Einstein metrics

Abstract

We present a renormalized Gauss-Bonnet formula for approximate Kahler-Einstein metrics on compact complex manifolds with pseudo-Einstein CR boundaries. The boundary integral is given explicitly, and it is proved that it gives a pseudo-Einstein invariant, which generalizes the Burns-Epstein invariant.

arXiv comment21 pages, some errors are corrected, an example is added