Fractional Poincaré inequality with finite total $Q$-curvature

Abstract

In this paper, we prove several Poincaré inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.

22 pages. arXiv admin note: text overlap with arXiv:1306.1841