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.
Conformal metrics with finite total Q-curvature revisited
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abstract
Given a conformal metric with finite total Q-curvature, we show that the assumptions on scalar curvature sensitively govern the Q-curvature integral. Additionally, we introduce a conformal mass for such manifolds. Using such mass, we provides a necessary and sufficient condition for the metric to be normal without assuming metric completeness. As applications, we derive volume comparison theorems and prove a positive mass type theorem related to Q-curvature.
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math.DG 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
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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.