Published Paper

Inserted: 12 jun 2018
Last Updated: 13 jun 2022

Journal: Communications in Analysis and Geometry
Volume: 27
Number: 8
Year: 2019
Doi: 10.4310/CAG.2019.v27.n8.a2

Abstract:

We generalise the classical Chern-Gauss-Bonnet formula to a class of 4-dimensional manifolds with finitely many conformally flat ends and singular points. This extends results of Chang-Qing-Yang in the smooth case. Under the assumptions of finite total Q curvature and positive scalar curvature at the ends and at the singularities, we obtain a new Chern-Gauss-Bonnet formula with error terms that can be expressed as isoperimetric deficits. This is the first such formula in a dimension higher than two which allows the underlying manifold to have isolated branch points or conical singularities.