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arXiv · 2206.06006

Prescribing $Q$-curvature on even-dimensional manifolds with conical singularities

Aleks Jevnikar·Yannick Sire·Wen Yang
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Abstract

On a $2m$-dimensional closed manifold we investigate the existence of prescribed $Q$-curvature metrics with conical singularities. We present here a general existence and multiplicity result in the supercritical regime. To this end, we first carry out a blow-up analysis of a $2m$th-order PDE associated to the problem and then apply a variational argument of min-max type. For $m>1$, this seems to be the first existence result for supercritical conic manifolds different from the sphere.

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Aleks Jevnikar, Yannick Sire, Wen Yang. 2022-06-13. Prescribing $Q$-curvature on even-dimensional manifolds with conical singularities. https://doi.org/10.4171/rmi%2F1543

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