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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.
Donaldson, Simon K.. "Interior estimates for solutions of Abreu's equation.." Collectanea Mathematica 56.2 (2005): 103-142. <http://eudml.org/doc/41824>.
@article{Donaldson2005, abstract = {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.}, author = {Donaldson, Simon K.}, journal = {Collectanea Mathematica}, keywords = {Geometría diferencial global; Variedades kählerianas; Toros geométricos; Ecuaciones en derivadas parciales no lineales; Monge-Ampère equation; Abreu's equation; a priori estimation of solutions; toric varieties; Kähler geometry}, language = {eng}, number = {2}, pages = {103-142}, title = {Interior estimates for solutions of Abreu's equation.}, url = {http://eudml.org/doc/41824}, volume = {56}, year = {2005}, }
TY - JOUR AU - Donaldson, Simon K. TI - Interior estimates for solutions of Abreu's equation. JO - Collectanea Mathematica PY - 2005 VL - 56 IS - 2 SP - 103 EP - 142 AB - 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. LA - eng KW - Geometría diferencial global; Variedades kählerianas; Toros geométricos; Ecuaciones en derivadas parciales no lineales; Monge-Ampère equation; Abreu's equation; a priori estimation of solutions; toric varieties; Kähler geometry UR - http://eudml.org/doc/41824 ER -