Geometric nonlinear problems and GIT stability through moment maps

Abstract

In this paper we re-visit the standard principle that if a geometric nonlinear PDE problem is set up in the moment map picture then the existence of the solution to the PDE should be related to GIT stability in algebraic geometry. We also take up Kähler metrics with constant Cahen–Gutt moment map and an extension of conformally Kähler, Einstein-Maxwell metrics.