May 16, 2024Open Access

Conformal metrics with finite total Q-curvature revisited

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Abstract

Given a conformal metric with finite total Q-curvature on Rⁿ for n4, we show that the sign of scalar curvature near infinity control not only the upper bound but also the lower bound of Q-curvature integral which is a new phenomenon. Meanwhile, for general complete non-compact four-manifolds with simple ends, we also obtain similar control of the lower bound of Q-curvature integral.

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Mingxiang Li (Thu,) studied this question.

synapsesocial.com/papers/68e69d5db6db643587622b1f https://doi.org/https://doi.org/10.48550/arxiv.2405.09872

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3Quantitative stability of the total $Q$-curvature near minimizing metrics2024
4Compactness of conformal metrics with constant $Q$-curvature of higher order2025
5New multiplicity results in prescribing <i>Q</i>-curvature on standard spheres2024

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