Singular solutions for the constant $Q$-curvature problem

TL;DR

This paper constructs weak singular solutions for the constant positive $Q$-curvature problem on closed manifolds, marking the first such achievement in high enough dimensions, advancing understanding of geometric analysis in conformal geometry.

Contribution

It introduces the first construction of singular metrics with constant positive $Q$-curvature on closed manifolds of sufficiently large dimension.

Findings

First construction of singular metrics with constant positive $Q$-curvature

Advances in methods for solving singular geometric PDEs

Extension of known solutions to higher-dimensional manifolds

Abstract

This paper is devoted to the construction of weak solutions to the singular constant $Q$-curvature problem. We build on several tools developed in the last years. This is the first construction of singular metrics on closed manifolds of sufficiently large dimension with constant (positive) $Q$-curvature.