Conformal metrics with finite total Q-curvature revisited

Mingxiang Li

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arXiv · 2405.09872

Conformal metrics with finite total Q-curvature revisited

Mingxiang Li

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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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Mingxiang Li. 2024-05-16. Conformal metrics with finite total Q-curvature revisited. https://arxiv.org/abs/2405.09872

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