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

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.

References in corpus (1)

• Future Directions of Research in Geometry: A Summary of the Panel Discussion at the 2007 Midwest Geometry Conference

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• The total Q-curvature, volume entropy and polynomial growth polyharmonic functions
• Variational theory for the resonant T-curvature equation