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

TL;DR

This paper establishes an explicit upper bound for the total Q-curvature and derives an isoperimetric deficit formula for complete conformal metrics on higher-dimensional Euclidean spaces with specific curvature conditions.

Contribution

It provides the first explicit upper bound for total Q-curvature and links it to isoperimetric deficits in higher-dimensional conformal geometry.

Findings

Explicit upper bound for total Q-curvature

Isoperimetric deficit formula derived

Applicable to complete conformal metrics with nonnegative scalar curvature

Abstract

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 $\mathbb R^n$, $n\ge 3$ with scalar curvature being nonnegative near infinity and Q-curvature being absolutely convergent.