Conformal metrics with finite total Q-curvature revisited

TL;DR

This paper investigates conformal metrics with finite total Q-curvature, establishing conditions under which the metric is normal, and introduces a conformal mass to derive volume comparison and positive mass theorems.

Contribution

It introduces a conformal mass for manifolds with finite total Q-curvature and provides new criteria for metric normality without completeness assumptions.

Findings

Scalar curvature assumptions influence Q-curvature integral

A conformal mass is defined for such manifolds

Volume comparison and positive mass theorems are established

Abstract

Given a conformal metric with finite total Q-curvature, we show that the assumptions on scalar curvature sensitively govern the Q-curvature integral. Additionally, we introduce a conformal mass for such manifolds. Using such mass, we provides a necessary and sufficient condition for the metric to be normal without assuming metric completeness. As applications, we derive volume comparison theorems and prove a positive mass type theorem related to Q-curvature.