On $L^\infty$ estimates for complex Monge-Ampère equations
Bin Guo, D. H. Phong, Freid Tong
Abstract
A PDE proof is provided for the sharp $L^\infty$ estimates for the complex Monge-Ampère equation that had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.
Topics & Concepts
MathematicsMonge–Ampère equationAmperePure mathematicsMathematical analysisApplied mathematicsCalculus (dental)Current (fluid)MedicineElectrical engineeringDentistryEngineeringGeometry and complex manifoldsGeometric Analysis and Curvature FlowsNonlinear Waves and Solitons