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

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 2mth-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.