An Upper Bound of the Total Q-Curvature and Its Isoperimetric Deficit for Higher-dimensional Conformal Euclidean Metrics

The aim of this paper is to give not only an explicit upper bound of the total Q-curvature but also an induced isoperimetric deficit formula for the complete conformal metrics on $mathbb R^n$, $nge 3$ with scalar curvature being nonnegative near infinity and Q-curvature being absolutely convergent.