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arXiv · 2512.24828

Bol's type inequality for singular metrics and its application to prescribing $Q$-curvature problems

Mrityunjoy Ghosh·Ali Hyder
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Abstract

In this article, we study higher-order Bol's inequality for radial normal solutions to a singular Liouville equation. By applying these inequalities along with compactness arguments, we derive necessary and sufficient conditions for the existence of radial normal solutions to a singular $Q$-curvature problem. Moreover, under suitable assumptions on the $Q$-curvature, we obtain uniform bounds on the total $Q$-curvature.

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Mrityunjoy Ghosh, Ali Hyder. 2025-12-31. Bol's type inequality for singular metrics and its application to prescribing $Q$-curvature problems. https://arxiv.org/abs/2512.24828

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