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The isoperimetric inequality and \(Q\)-curvature. (English) Zbl 1323.52008

Author’s abstract: A well-known question in differential geometry is to control the constant in isoperimetric inequality by intrinsic curvature conditions. In dimension 2, the constant can be controlled by the integral of the positive part of the Gaussian curvature. In this paper, we show that on simply connected conformally flat manifolds of higher dimensions, the role of the Gaussian curvature can be replaced by the Branson’s \(Q\)-curvature. We achieve this by exploring the relationship between \(A_p\) weights and integrals of the \(Q\)-curvature.

MSC:

52B60 Isoperimetric problems for polytopes
42B35 Function spaces arising in harmonic analysis
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