Calculus of Variations and Geometric Measure Theory

R. Buzano - H. T. Nguyen

The higher-dimensional Chern-Gauss-Bonnet formula for singular conformally flat manifolds

created by muller on 12 Jun 2018
modified on 13 Jun 2022


Published Paper

Inserted: 12 jun 2018
Last Updated: 13 jun 2022

Journal: Journal of Geometric Analysis
Volume: 29
Year: 2019
Doi: 10.1007/s12220-018-0029-z

ArXiv: 1703.05723 PDF


In a previous article, we generalised the classical four-dimensional Chern-Gauss-Bonnet formula to a class of manifolds with finitely many conformally flat ends and singular points, in particular obtaining the first such formula in a dimension higher than two which allows the underlying manifold to have isolated conical singularities. In the present article, we extend this result to all even dimensions $n\geq 4$ in the case of a class of conformally flat manifolds.