May 28, 2021
Singular metrics of constant non-local curvature.
We will consider the problem of constructing singular metrics of constant non-local curvature in conformal geometry, using a gluing scheme. This non-local curvature is defined from the conformal fractional Laplacian, a Paneitz type operator of non-integer order. For the gluing process, one needs a model solution which is given by the solution of a non-local ODE with good conformal properties. It turns out that conformal geometry provides powerful tools for the analysis of such equations.