Conformal metrics with finite total Q-curvature revisited

Abstract

Given a conformal metric with finite total Q-curvature on $\mathbb{R}^n$ for $n\geq4$, 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.

Locations

• arXiv (Cornell University) - View - PDF