Calculus of Variations and Geometric Measure Theory
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R. Buzano - H. T. Nguyen

The Chern-Gauss-Bonnet formula for singular non-compact four-dimensional manifolds

created by muller on 12 Jun 2018



Inserted: 12 jun 2018
Last Updated: 12 jun 2018

Year: 2015

ArXiv: 1503.06602 PDF


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.

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