In this talk, we discuss the regularity of the solutions u to the complex Monge-Ampére equation that are uniformly close to quadratic polynomials. Our main tool is Savin’s small perturbation theorem. By study these solutions, we produce two regularity results for the complex Monge-Ampére equation.
The ?rst result is a Liouville-type theorem. It considers uniqueness of the global solutions on $mathbb{C}^{n}$ with certain growth at infinity. The second result is a $C^{2,alpha}$-estimate of $W^{2,p}$-solutions. It is a perturbation result of Blocki-Dinew’s estimate of $W^{2,p}$-solutions.
Speaker: Yu Wang, Department of Mathematics, Columbia University