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Existence of complete conformal metrics on $\mathbb{R}^n$ with prescribed Q-curvature

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arxiv 2503.23689 v1 pith:SS4QZT64 submitted 2025-03-31 math.DG math.AP

Mingxiang Li , Biao Ma This is my paper · ORCID
classification math.DGmath.AP
keywords q-curvaturecompleteconformalmathbbequalsexistenceexistsfinite
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abstract

Given a smooth function $f(x)$ on $\mathbb{R}^n$ which is positive somewhere and satisfies $f(x)=O(|x|^{-l})$ for any $l>\frac{n}{2}$, we show that there exists a complete and conformal metric $g=e^{2u}|dx|^2$ with finite total Q-curvature such that its Q-curvature equals to $f(x)$.

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Cited by 1 Pith paper

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  1. Multiple Blow-Up Phenomena for $Q$-Curvature in High Dimensions

    math.DG 2025-12 conditional novelty 6.0 of 10

    In dimensions n≥25, constant Q-curvature metrics can have arbitrarily large energy and unbounded volume, with multiple concentrating bubbles.

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