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Higher order Bol's inequality and its applications
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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).
Forward citations
Cited by 2 Pith papers
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Sharp weighted Carleman and Huber isoperimetric inequalities on the unit ball in higher dimensions
New sharp weighted Carleman inequalities with extremal classification are proved in all dimensions, and a sharp weighted Huber isoperimetric inequality is established in even dimensions.
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Bonnet-Myers type theorems for $Q$-curvature on four-manifolds
Complete four-manifolds with R ≥ c>0 and Q ≥ c'>0 are compact; if Q/R ≥ k>0 then diameter ≤ 4π/√(15k).
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