Conformal metrics with finite total Q-curvature revisited

Given a conformal metric with finite total Q-curvature on Rⁿ for n≥4, we show that the sign of scalar curvature near infinity control not only the upper bound but also the lower bound of Q-curvature integral which is a new phenomenon. Meanwhile, for general complete non-compact four-manifolds with simple ends, we also obtain similar control of the lower bound of Q-curvature integral.