This paper develops various estimates for solutions of a nonlinear, fouth order PDE which corresponds to prescribing the scalar curvature of a toric Kähler metric. The results combine techniques from Riemannian geometry and from the theory of Monge-Ampère equations.
@article{urn:eudml:doc:41824, title = {Interior estimates for solutions of Abreu's equation.}, journal = {Collectanea Mathematica}, volume = {56}, year = {2005}, pages = {103-142}, zbl = {1085.53063}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41824} }
Donaldson, Simon K. Interior estimates for solutions of Abreu's equation.. Collectanea Mathematica, Tome 56 (2005) pp. 103-142. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41824/