In this paper, we study the ends of a locally conformally flat complete manifold with finite total Q-curvature. We prove that for such a manifold, the integral of the Q-curvature equals an integral multiple of a dimensional constant $$c_n$$ c n , where $$c_n$$ c n is the integral of the Q-curvature on the unit n-sphere. It provides further evidence that the Q-curvature on a locally conformally flat manifold controls geometry as the Gaussian curvature does in two dimension.
Calculus of Variations and Partial Differential Equations – Springer Journals
Published: Jun 16, 2017
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