On the Chern-Gauss-Bonnet integral for conformal metrics on R4

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Existence of conformal metrics with constant Q-curvature (2004, background): “…that the Paneitz operator and the Q -curvature (together with their higher-dimensional analogues, see [5], [6], [26], [27]) appear in the study of Moser-Trudinger type inequalities, log-determinant formulas and the compactiﬁcation of locally conformally ﬂat manifolds, [7], [8], [14], [15], [16].”
Compactness of solutions to some geometric fourth-order equations (2004, background): “Finally, we also point out that the Paneitz operator and the Q-curvature (together with their higherdimensional analogues, see [5], [6], [27], [29]) appear in the study of Moser-Trudinger type inequalities, log-determinant formulas and the compactification of locally conformally flat manifolds, see ”
PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT (2001, background): “tz operator and related topics have been recently obtained by several authors. Among them, let us mention Branson [9], Branson-Chang-Yang [11], Chang-Yang [20], ChangGursky-Yang [15], Chang-Qing-Yang [16] and [17], Gursky [27]. See also the surveys Chang [13] and ChangYang [18] for more results on b”
Compactification of a class of conformally flat 4-manifold (2000, methodology): “Since Lemma 1.8 below can be proved following the same outline as the corresponding lemma: Lemma 3.1 in [ CQY ], we will skip its proof here.”