香蕉视频

Title: Monge-Ampere equation with bounded periodic data

Abstract: We consider the Monge-Ampere equation det(D^2u) = f in R^n, where f is a positive bounded periodic function. We prove that u must be the sum of a quadratic polynomial and a periodic function. For f =1, this is the classic result by Jorgens, Calabi and Pogorelov. For f \in C^\alpha, this was proved by Caffarelli and Li. This is a joint work with Y.Y. Li.