Connected sums of closed Riemannian manifolds and fourth-order conformal invariants (Q1951201)

The Yamabe problem in differential geometry concerns the existence of Riemannian metrics with constant scalar curvature. A complete solution of this problem was given by \textit{R. Schoen} in [J. Differ. Geom. 20, 479--495 (1984; Zbl 0576.53028)]. In the present paper, the author studies the fourth-order analogue of the Yamabe problem in conformal geometry. The tools of study are Paneitz constants and Paneitz invariants, which are the counterparts of the Yamabe constants and Yamabe invariants.