Calculus of Variations and Geometric Measure Theory

A. Jevnikar - Y. Sire - W. Yang

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

created by jevnikar on 13 Jun 2022



Inserted: 13 jun 2022
Last Updated: 13 jun 2022

Year: 2022


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.

Keywords: Variational methods, blow-up analysis, conical singularities, $Q$-curvature