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

TL;DR

This paper develops a renormalized Gauss-Bonnet formula for approximate Kahler-Einstein metrics on complex manifolds with pseudo-Einstein CR boundaries, introducing a boundary invariant that generalizes known invariants.

Contribution

It introduces a new renormalized Gauss-Bonnet formula and explicitly characterizes the boundary integral as a pseudo-Einstein invariant, extending previous invariants.

Findings

Boundary integral explicitly given

Boundary integral defines a pseudo-Einstein invariant

Generalizes the Burns-Epstein invariant

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.