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arXiv · 2308.11388

Higher order Bol's inequality and its applications

Mingxiang Li·Juncheng Wei
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Abstract

In the conformal class of Euclidean space, we give some volume comparison theorems with help of Q-curvature. Meanwhile, for compact four dimensional manifolds with non-negative scalar curvature, we give a volume rigidity theorem with respect to Q-curvature. Finally, we make use of these results to give some sufficient and necessary conditions for the existence of solutions to some conformally invariant equations which answers an open problem raised by Hyder-Martinazzi (2021, JDE).

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Mingxiang Li, Juncheng Wei. 2023-08-22. Higher order Bol's inequality and its applications. https://arxiv.org/abs/2308.11388

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