Poisson equations, uniformization, and geometrical optics (Q2786826)

In this article, the Poisson equation \(\Delta_g u=f\) is studied on a variety of noncompact Riemannian manifolds \(M\). Here, \(f\) is either compactly supported or it possesses a simple asymptotic expansion at infinity. The study of this equation is motivated by a construction in geometrical optics provided that \(M\) is a compactly perturbed plane and \(f\) has compact support. The author's results in turn motivate a study for higher dimensional \(M\) and more general \(f\).NEWLINENEWLINEFor the entire collection see [Zbl 1322.53004].