Non-negative top-order Q-curvature of a complete normal conformal metric on R^n forces non-negative sectional curvature, yielding a sharp isoperimetric inequality with deficit equal to the normalized total Q-curvature.
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A sharp isoperimetric inequality and the top order $Q$-curvature
Non-negative top-order Q-curvature of a complete normal conformal metric on R^n forces non-negative sectional curvature, yielding a sharp isoperimetric inequality with deficit equal to the normalized total Q-curvature.